Tuesday, January 28, 2020
Maxima And Minima Of Functions Mathematics Essay
Maxima And Minima Of Functions Mathematics Essay Maxima and Minima are important topics of maths Calculus. It is the approach for finding maximum or minimum value of any function or any event. It is practically very helpful as it helps in solving the complex problems of science and commerce. It can be with one variable of with more than one variable. These can be done with the help of simple geometry and math functions. Finding the maxima and minima, both absolute and relative, of various functions represents an important class of problems solvable by use of differential calculus. The theory behind finding maximum and minimum values of a function is based on the fact that the derivative of a function is equal to the slope of the tangent. Analytical definition A real-valued function f defined on a real line is said to have a local (or relative) maximum point at the point xà ¢Ã‹â€ -, if there exists some ÃŽÂ µ > 0 such that f(xà ¢Ã‹â€ -) à ¢Ã¢â‚¬ °Ã‚ ¥ f(x) when |x à ¢Ã‹â€ ’ xà ¢Ã‹â€ -| Restricted domains: There may be maxima and minima for a function whose domain does not include all real numbers. A real-valued function, whose domain is any set, can have a global maximum and minimum. There may also be local maxima and local minima points, but only at points of the domain set where the concept of neighbourhood is defined. A neighbourhood plays the role of the set of x such that |x à ¢Ã‹â€ ’ xà ¢Ã‹â€ -| A continuous (real-valued) function on a compact set always takes maximum and minimum values on that set. An important example is a function whose domain is a closed (and bounded) interval of real numbers (see the graph above). The neighbourhood requirement precludes a local maximum or minimum at an endpoint of an interval. However, an endpoint may still be a global maximum or minimum. Thus it is not always true, for finite domains, that a global maximum (minimum) must also be a local maximum (minimum). Finding Functional Maxima And Minima Finding global maxima and minima is the goal of optimization. If a function is continuous on a closed interval, then by the extreme value theorem global maxima and minima exist. Furthermore, a global maximum (or minimum) either must be a local maximum (or minimum) in the interior of the domain, or must lie on the boundary of the domain. So a method of finding a global maximum (or minimum) is to look at all the local maxima (or minima) in the interior, and also look at the maxima (or minima) of the points on the boundary; and take the biggest (or smallest) one. Local extrema can be found by Fermats theorem, which states that they must occur at critical points. One can distinguish whether a critical point is a local maximum or local minimum by using the first derivative test or second derivative test. For any function that is defined piecewise, one finds maxima (or minima) by finding the maximum (or minimum) of each piece separately; and then seeing which one is biggest (or smallest). Examples The function x2 has a unique global minimum at x = 0. The function x3 has no global minima or maxima. Although the first derivative (32) is 0 at x = 0, this is an inflection point. The function x-x has a unique global maximum over the positive real numbers at x = 1/e. The function x3/3 à ¢Ã‹â€ ’ x has first derivative x2 à ¢Ã‹â€ ’ 1 and second derivative 2x. Setting the first derivative to 0 and solving for x gives stationary points at à ¢Ã‹â€ ’1 and +1. From the sign of the second derivative we can see that à ¢Ã‹â€ ’1 is a local maximum and +1 is a local minimum. Note that this function has no global maximum or minimum. The function |x| has a global minimum at x = 0 that cannot be found by taking derivatives, because the derivative does not exist at x = 0. The function cos(x) has infinitely many global maxima at 0,  ±2à ₠¬,  ±4à ₠¬, à ¢Ã¢â€š ¬Ã‚ ¦, and infinitely many global minima at  ±Ãƒ â‚ ¬,  ±3à ₠¬, à ¢Ã¢â€š ¬Ã‚ ¦. The function 2 cos(x) à ¢Ã‹â€ ’ x has infinitely many local maxima and minima, but no global maximum or minimum. The function cos(3à ₠¬x)/x with 0.1 à ¢Ã¢â‚¬ °Ã‚ ¤Ã‚ x à ¢Ã¢â‚¬ °Ã‚ ¤Ã‚ 1.1 has a global maximum at x = 0.1 (a boundary), a global minimum near x = 0.3, a local maximum near x = 0.6, and a local minimum near x = 1.0. (See figure at top of page.) The function x3 + 32 à ¢Ã‹â€ ’ 2x + 1 defined over the closed interval (segment) [à ¢Ã‹â€ ’4,2] has two extrema: one local maximum at x = à ¢Ã‹â€ ’1à ¢Ã‹â€ ’à ¢Ã‹â€ Ã… ¡15à ¢Ã‚ „3, one local minimum at x = à ¢Ã‹â€ ’1+à ¢Ã‹â€ Ã… ¡15à ¢Ã‚ „3, a global maximum at x = 2 and a global minimum at x = à ¢Ã‹â€ ’4. Functions of more than one variable  For functions of more than one variable, similar conditions apply. For example, in the (enlargeable) figure at the right, the necessary conditions for a local maximum are similar to those of a function with only one variable. The first partial derivatives as to z (the variable to be maximized) are zero at the maximum (the glowing dot on top in the figure). The second partial derivatives are negative. These are only necessary, not sufficient, conditions for a local maximum because of the possibility of a saddle point. For use of these conditions to solve for a maximum, the function z must also be differentiable throughout. The second partial derivative test can help classify the point as a relative maximum or relative minimum. In contrast, there are substantial differences between functions of one variable and functions of more than one variable in the identification of global extrema. For example, if a differentiable function f defined on the real line has a single critical point, which is a local minimum, then it is also a global minimum (use the intermediate value theorem and Rolles Theorem to prove this by reduction ad absurdum). In two and more dimensions, this argument fails, as the function shows. Its only critical point is at (0,0), which is a local minimum with Æ’(0,0) = 0. However, it cannot be a global one, because Æ’(4,1) = à ¢Ã‹â€ ’11. The global maximum is the point at the top In relation to sets Maxima and minima are more generally defined for sets. In general, if an ordered set S has a greatest element m, m is a maximal element. Furthermore, if S is a subset of an ordered set T and m is the greatest element of S with respect to order induced by T, m is a least upper bound of S in T. The similar result holds for least element, minimal element and greatest lower bound. In the case of a general partial order, the least element (smaller than all other) should not be confused with a minimal element (nothing is smaller). Likewise, a greatest element of a partially ordered set (poset) is an upper bound of the set which is contained within the set, whereas a maximal element m of a poset A is an element of A such that if m à ¢Ã¢â‚¬ °Ã‚ ¤ b (for any b in A) then m = b. Any least element or greatest element of a poset is unique, but a poset can have several minimal or maximal elements. If a poset has more than one maximal element, then these elements will not be mutually comparable. In a totally ordered set, or chain, all elements are mutually comparable, so such a set can have at most one minimal element and at most one maximal element. Then, due to mutual comparability, the minimal element will also be the least element and the maximal element will also be the greatest element. Thus in a totally ordered set we can simply use the terms minimum and maximum. If a chain is finite then it will always have a maximum and a minimum. If a chain is infinite then it need not have a maximum or a minimum. For example, the set of natural numbers has no maximum, though it has a minimum. If an infinite chain S is bounded, then the closure Cl(S) of the set occasionally has a minimum and a maximum, in such case they are called the greatest lower bound and the least upper bound of the set S, respectively. The diagram below shows part of a function y = f(x). The Point A is a local maximum and the Point B is a local minimum. At each of these points the tangent to the curve is parallel to the x-axis so the derivative of the function is zero. Both of these points are therefore stationary points of the function. The term local is used since these points are the maximum and minimum in this particular region. There may be others outside this region. function f(x) is said to have a local maximum at x = a, if $ is a neighbourhood I of a, such that f(a) f(x) for all x I. The number f(a) is called the local maximum of f(x). The point a is called the point of maxima. Note that when a is the point of local maxima, f(x) is increasing for all values of x a in the given interval. At x = a, the function ceases to increase. A function f(x) is said to have a local minimum at x = a, if $ is a neighbourhood I of a, such that f(a) f(x) for all x I Here, f(a) is called the local minimum of f(x). The point a is called the point of minima. Note that, when a is a point of local minimum f (x) is decreasing for all x a in the given interval. At x = a, the function ceases to decrease. If f(a) is either a maximum value or a minimum value of f in an interval I, then f is said to have an extreme value in I and the point a is called the extreme point. Monotonic Function maxima and minima A function is said to be monotonic if it is either increasing or decreasing but not both in a given interval. Consider the function The given function is increasing function on R. Therefore it is a monotonic function in [0,1]. It has its minimum value at x = 0 which is equal to f (0) =1, has a maximum value at x = 1, which is equal to f (1) = 4. Here we state a more general result that, Every monotonic function assumes its maximum or minimum values at the end points of its domain of definition. Note that every continuous function on a closed interval has a maximum and a minimum value. Theorem on First Derivative Test (First Derivative Test) Let f (x) be a real valued differentiable function. Let a be a point on an interval I such that f (a) = 0. (a) a is a local maxima of the function f (x) if i) f (a) = 0 ii) f(x) changes sign from positive to negative as x increases through a. That is, f (x) > 0 for x f (x) a (b) a is a point of local minima of the function f (x) if i) f (a) = 0 ii) f(x) changes sign from negative to positive as x increases through a. That is, f (x) f (x) > 0 for x > a Working Rule for Finding Extremum Values Using First Derivative Test Let f (x) be the real valued differentiable function. Step 1: Find f (x) Step 2: Solve f (x) = 0 to get the critical values for f (x). Let these values be a, b, c. These are the points of maxima or minima. Arrange these values in ascending order. Step 3: Check the sign of f'(x) in the immediate neighbourhood of each critical value. Step 4: Let us take the critical value x= a. Find the sign of f (x) for values of x slightly less than a and for values slightly greater than a. (i) If the sign of f (x) changes from positive to negative as x increases through a, then f (a) is a local maximum value. (ii) If the sign of f (x) changes from negative to positive as x increases through a, then f (a) is local minimum value. (iii) If the sign of f (x) does not change as x increases through a, then f (a) is neither a local maximum value not a minimum value. In this case x = a is called a point of inflection. Maxima and Minima Example Find the local maxima or local minima, if any, for the following function using first derivative test f (x) = x3 62 + 9x + 15 Solution to Maxima and Minima Example f (x) = x3 62 + 9x + 15 f (x) = 32 -12x + 9 = 3(x2- 4x + 3) = 3 (x 1) (x 3) Thus x = 1 and x = 3 are the only points which could be the points of local maxima or local minima. Let us examine for x=1 When x f (x) = 3 (x 1) (x 3) = (+ ve) (- ve) (- ve) = + ve When x >1 (slightly greater than 1) f (x) = 3 (x -1) (x 3) = (+ ve) (+ ve) (- ve) = ve The sign of f (x) changes from +ve to -ve as x increases through 1. x = 1 is a point of local maxima and f (1) = 13 6 (1)2 + 9 (1) +15 = 1- 6 + 9 + 15 =19 is local maximum value. Similarly, it can be examined that f (x) changes its sign from negative to positive as x increases through the point x = 3. x = 3 is a point of minima and the minimum value is f (3) = (3)3- 6 (3)2+ 9(3) + 15 = 15 Theorem on Second Derivative Test Let f be a differentiable function on an interval I and let a I. Let f (a) be continuous at a. Then i) a is a point of local maxima if f (a) = 0 and f (a) ii) a is a point of local minima if f (a) = 0 and f (a) > 0 iii) The test fails if f (a) = 0 and f (a) = 0. In this case we have to go back to the first derivative test to find whether a is a point of maxima, minima or a point of inflexion. Working Rule to Determine the Local Extremum Using Second Derivative Test Step 1 For a differentiable function f (x), find f (x). Equate it to zero. Solve the equation f (x) = 0 to get the Critical values of f (x). Step 2 For a particular Critical value x = a, find f (a) (i) If f (a) (ii) If f (a) > 0 then f (x) has a local minima at x = a and f (a) is the minimum value. (iii) If f (a) = 0 or , the test fails and the first derivative test has to be applied to study the nature of f(a). Example on Local Maxima and Minima Find the local maxima and local minima of the function f (x) = 23 212 +36x 20. Find also the local maximum and local minimum values. Solution: f (x) = 62 42x + 36 f (x) = 0 x = 1 and x = 6 are the critical values f (x) =12x 42 If x =1, f (1) =12 42 = 30 x =1 is a point of local maxima of f (x). Maximum value = 2(1)3 21(1)2 + 36(1) 20 = -3 If x = 6, f (6) = 72 42 = 30 > 0 x = 6 is a point of local minima of f (x) Minimum value = 2(6)3 21 (6)2 + 36 (6)- 20 = -128 Absolute Maximum and Absolute Minimum Value of a Function Let f (x) be a real valued function with its domain D. (i) f(x) is said to have absolute maximum value at x = a if f(a)  ³ f(x) for all x ÃŽ D. (ii) f(x) is said to have absolute minimum value at x = a if f(a)  £ f(x) for all x ÃŽ D. The following points are to be noted carefully with the help of the diagram. Let y = f (x) be the function defined on (a, b) in the graph. (i) f (x) has local maximum values at x = a1, a3, a5, a7 (ii) f (x) has local minimum values at x = a2, a4, a6, a8 (iii) Note that, between two local maximum values, there is a local minimum value and vice versa. (iv) The absolute maximum value of the function is f(a7)and absolute minimum value is f(a). (v) A local minimum value may be greater than a local maximum value. Clearly local minimum at a6 is greater than the local maximum at a1. Theorem on Absolute Maximum and Minimum Value Let f be a continuous function on an interval I = [a, b]. Then, f has the absolute maximum value and f attains it at least once in I. Also, f has the absolute minimum value and attains it at least once in I. Theorem on Interior point in Maxima and Minima Let f be a differentiable function on I and let x0 be any interior point of I. Then (a) If f attains its absolute maximum value at x0, then f (x0)= 0 (b) If f attains its absolute minimum value at x0, then f (x0) = 0. In view of the above theorems, we state the following rule for finding the absolute maximum or absolute minimum values of a function in a given interval. Step 1: Find all the points where f takes the value zero. Step 2: Take the end points of the interval. Step 3: At all the points calculate the values of f. Step 4: Take the maximum and minimum values of f out of the values calculated in step 3. These will be the absolute maximum or absolute minimum values. Real life Problem Solving With Maxima And Minima For a belt drive the power transmitted is a function of the speed of the belt, the law being P(v) = Tv av3 where T is the tension in the belt and a some constant. Find the maximum power if T = 600, a = 2 and v 12. Is the answer different if the maximum speed is 8? Solution First find the critical points. P = 600v 2v3 And so = 600 6v2 This is zero when v =  ±10. Commonsense tells us that v 0, and so we can forget about the critical point at -10. So we have just the one relevant critical point to worry about, the one at x = 10. The two endpoints are v = 0 and v = 12. We dont hold out a lot of hope for v = 0, since this would indicate that the machine was switched off, but we calculate it anyway. Next calculate P for each of these values and see which is the largest. P(0) = 0 ,        P(10) = 6000 2000 = 4000 ,        P(12) = 7200 3456 = 3744 So the maximum occurs at the critical point and is 4000. When the range is reduced so that the maximum value of v is down to 8, neither of the critical points is in range. That being the case, we just have the endpoints to worry about. The maximum this time is P(8) = 4800 1024 = 3776. A box of maximum volume is to be made from a sheet of card measuring 16 inches by 10. It is an open box and the method of construction is to cut a square from each corner and then fold. Solution Let x be the side of the square which is cut from each corner. Then AB = 16 2x, CD = 10 2x and the volume, V, is given by V = (16 2x)(10 2x)x = 4x(8 x)(5 x) And so = 4(x3-132+40x) =4(32-26x+40) The critical points occur when 32 26x + 40 = 0 i.e. when x =  = The commonsense restrictions are 5 x 0.So the only critical point in range is x = 2. Now calculate V for the critical point and the two endpoints. V(0) = 0 ,        V(2) = 144 ,        V(5) = 0 So the maximum value is 144, occurring when x = 2. Uses of Maxima and Minima in War. Concepts of maxima and minima can be used in war to predict most probably result of any event. It can be very helpful to all soldiers as it help to save time. Maximum damage with minimum armor can be predicted via these functions. It can be helpful in preventive actions for military. It is use dto calculate ammunition numbers, food requests, fuel consumption, parts ordering, and other logical operations. It is also helpful in finding daily expenditure on war.
Sunday, January 19, 2020
An Alternate Perspective on the Mythical West :: essays papers
An Alternate Perspective on the Mythical West The topic of the American West has intrigued me throughout my life. The tales of cowboys and Indians, of the rugged individual and nature, has always sparked my interest. A land with such quixotic stories of adventure, the West has instilled itself in American history. The yarns and movies of the mythical frontier provide a perception to which I among many others have chosen to adopt at one time or another. This perception has been embedded in many youths, providing a nationalistic view of America using the West as a symbol of the individualism to which our forefathers fought for. Yet it is human nature to be inquisitive, and so I delved into this topic in the hopes of developing a better understanding of the history of the great American frontier. The myth of the American West has been intertwined throughout United States history. It is often perceived as a romantic story, a legacy that has ingrained itself in American culture and society. The 1890 census announced the end of the frontier, closing a chapter in American history. In 1893, Frederick Jackson Turner argued the importance of the frontier in shaping American politics, economy, and culture. Turner’s nationalistic view of the West created a problem, providing a mythical notion of a realistically rough arena filled with conflict and frustration. Furthermore, the thesis proposed by Turner proved to be futile for the present and future. The firmness of Turner’s thesis left it susceptible to challenges, creating a revolution of historical study of the Old West in the mid-twentieth century. Historians dedicated to the American West have branched off from Turner and have created a field that hinges on this complex area. These historians have challenged the old myths of a quaint West, seeking to expose the true nature of Western expansion. Among these historians, Patricia Nelson Limerick has developed a perception of the West based on the stories of the men and women who actually lived there. In her book, The Legacy of Conquest: The Unbroken Past of the American West, Limerick maintains that Westward expansion was not a romantic saga of cowboys and Indians, but instead was a gradual conquest based on economics and politics. In a sense, the West was not founded by rugged individualists, but rather by competition and profit.
Saturday, January 11, 2020
Physician-Assisted Suicide (PAS)
Why would anyone consider Physician-Assisted Suicide (PAS)? It’s a scenario that’s seen all too oftenâ€â€a chronically ill woman is suffering in severe excruciating pain daily and feels like she’s become a burden to her family, a lonely man is suffering with a life-limiting illness and has no family to offer any care or support to him. These individuals have lost their independence and feel like they have no quality of life left to live. Great strides have been made to improve end-of-life care through palliative care and hospice programs, but sometimes that’s just not enough. In America, the care that is offered to the elderly and the chronically ill is less than ideal. Statistics show that an estimated 40-70% of patients die in pain and another 50-60% die feeling shortness of breath. Ninety percent of the nursing homes where patients go to receive 24-hour nursing care are seriously understaffed. Patients who are home and have care provided by family o ften feel like they are a burden on their caregivers. The cost of hiring in-home caregivers support is not covered by Medicare or state and federal Medicaid systems. Caregivers often suffer from physical, emotional, financial, psychological and social strain. A person may feel as if they have lost all control of their life when they suffer from chronic and life-limiting illnesses. The body isn’t doing what it should and there is no way to stop it.Therefore, a person my feel like they can regain some control through Physician-Assisted Suicide (PAS). If they can’t control the illness, they can at least control the way they die. Suffering has always been a part of human existence. Since the beginning of medicine there have been requests made to end this suffering by means of physician-assisted suicide.Physician-assisted suicide is when a patient voluntarily choses to terminate their own life by the administration of a legal substance with the assistance of a physician eit her directly or indirectly. The patient is provided a medical means and/or knowledge to commit suicide by a physician. The life-ending act is performed by the patient and not the physician. Recent studies show that approximately 57% of physicians practicing today have received a request for physician-assisted suicide in some form or another.There are many alternatives to PAS that exist. Unrelieved physical suffering may have been greater in the past, but now modern medicine has more knowledge and skills to relieve suffering than ever before. If all patients had access to careful assessment and optimal symptom control and supportive care, palliative care specialists believe that most patients with life-threatening illnesses suffering could be sufficiently reduced to eliminate their desire for a quick death. When the patient’s desire prevails, there are other available avenues to relieve the suffering and avoid prolonging life against their wishes. The driving force behind p atients seeking physician-assisted suicide is quality of life.In October 1997, physician-assisted suicide became legal in the state of Oregon. By the end of the year 2000, approximately 70 people had utilized the physician-assisted suicide law to end their lives. One hundred percent of these cases reported that individuals were not able to take care for themselves and make their own decisions and loss of autonomy. Eighty-six percent of these cases reported that individuals were suffering from loss of dignity and the ability to participate in enjoyable activities.Currently, physician-assisted suicide is legal in Oregon, Washington, Vermont and Montana. Oregon was the first to pass the Death with Dignity Act in 1997. The requirements for attending/prescribing or consulting with a physician to write a prescription are listed in the following table. Washington followed suit passing the Death with Dignity Act in 2008, and Montana passed the Rights of Terminally III Act in 2009.Table 1. S afeguards and Guidelines in the Oregon Act1. Requires the patient give a fully informed, voluntary decision. 2. Applies only to the last 6 months of the patient’s life. 3. Makes it mandatory that a second opinion by a qualified physician be given that the patient has fewer than 6 months to live. 4. Requires two oral requests by the patient.5. Requires a written request by the patient. 6. Allows cancellation of the request at any time. 7. Makes it mandatory that a 15-day waiting period occurs after the first oral request. 8. Makes it mandatory that 48-hours (2 days) elapse after the patient makes a written request to receive the medication. 9. Punishes anyone who uses coercion on a patient to use the Act. 10. Provides for psychological counseling if either of the patient’s physicians thinks the patient needs counseling. 11. Recommends the patient inform his/her next of kin.12. Excludes nonresidents of Oregon from taking part. 13. Mandates participating physicians are li censed in Oregon. 14. Mandates Health Division Review. 15. Does not authorize mercy killing or active euthanasia. Source: Compassion & Choices of Oregon, 2009b.Physician-assisted suicide is illegal in Canada. In the Netherlands, it is legal under certain circumstances, and the right to choose physician-assisted suicide remains highly favored. Physician-assisted suicide is also illegal in the United Kingdom. They currently focus on palliative care. Under strictly defined regulations, physician-assisted suicide is legal in the following countries: Australia, Columbia, and Japan. The legalization of physician-assisted suicide remains controversial.The topic periodically comes up for intense attention. Organized medicine agrees on two principles: 1. Physicians have an obligation to relieve pain and suffering and to promote the dignity of dying patients in their care. 2. The principle of patient bodily integrity requires that physicians must respect patients’ competent decisions t o forgo life-sustaining treatment. There are four main points argued against the acceptance and legalization of physician-assisted suicide along with their counter argument. Improved Access to Hospice and Palliative CareWith quality end-of-life care being made available through hospice and palliative care programs, there is no reason for anyone to seek physician-assisted suicide. In the United States, there are over 4,500 hospice agencies. Millions of people don’t have access to the hospice agencies because of the restrictions on funding and the inflexibility of the Medicare Hospice Benefit requiring patients to have a life expectancy of six months or less. Counter argument: Rare cases of persistent and untreatable suffering will still exist even with improved access to quality end-of-life care. Hospice and palliative care aren’t always sufficient to treat severe suffering. Limits on Patient AutonomyPhysician-assisted suicide requires the assistance of another perso n. In the opinion of Bouvia vs. Superior Court, â€Å"the right to dies is an integral part of our right to control our own destinies so long as the rights of others are not affected,†was determined. Our society threatens physician-assisted suicide by worsening the value of human life. The sanctity of life is the responsibility of society to preserve it. Counter argument: Physicians who are requested to help to end a patients’ life have the right to decline on the basis of conscientious objection. The â€Å"Slippery Slope†to Social DepravityThere is concern to the opposition to physician-assisted suicide being allowed with euthanasia not too far behind. Without the consent of individuals in physical handicap, the elderly, the demented, the individuals with mental illness, and the homeless, there is a slippery slope toward euthanasia without the consent of the individuals is deemed â€Å"useless†by society. Counter argument: The â€Å"slippery slopeâ⠂¬ would not be allowed to happen within our highly cultured societies. Violation of the Hippocratic OathThe Hippocratic Oath states that a physician’s obligation is primum non nocere, â€Å"first, do no harm.†The direct contrast to that is physician-assisted suicide, where killing a patient is deliberately regarded as harm. Counter argument: According to an individual patient’s needs, the Hippocratic Oath should not be interpreted. Alternatives to Physician-Assisted SuicideThose opposing to physician-assisted suicide argue that there are legal and morally ethical alternatives to assisted death. Patients have the right to refuse any further medical treatments that may prolong the death, including the medications. Counter argument: Life-sustaining measures to live and still suffer are not relied on by some patients. Withholding life-sustaining treatments would only prolong suffering for these patients. Another argument is that patients can, and often do, de cide to stop eating and drinking to speed up their death. Within one to three weeks afterwards, the death will usually occur, and it would be reported as a â€Å"good death.†Counter argument: One to three weeks of intense suffering is too much for any one person to have to put up with. This debate has yet to see any final resolution. Physician-assisted suicide may become more of a reality in our society because of the undercurrent of public support. The United States Supreme Court handed down two cases central to physician-assisted suicide in 1997: Vacco vs. Quill and Gregoire vs. Glucksberg. In both case, it was determined that there was no constitutional right on the grounds of equal protection or personal liberty to the physician-assisted suicide. Both constitutional history and the Western Civilization trends were argued by the court and generally worked against reading the Constitution that way.The court was sensitive in its decision to the prospect of unintended and unw anted consequences that might follow the recognition of a Constitutional right to physician-assisted suicide. However, it was never said that physician-assisted suicide would ever be legitimate. It was concluded that the states of the Union could decide the matter for themselves. Requests for physician-assisted suicide should be taken very seriously. Responses to these requests should be compassionate and immediate. There are six steps that should physicians should take when responding to requests for physician-assisted suicides: Step 1: Clarify the RequestStep 2: Determine the Root Causes Step 3: Affirm Your Commitment to Care for the Patient Step 4: Address the Root Causes of the Request Step 5: Educate the Patient About Legal Alternatives for Comfort and Control Step 6: Seek Counseling from Trusted Colleagues and AdvisorsStep 1: Clarify the RequestThe physician should talk to the patient about what suffering means to them. Determine if their point of view can be defined. Listen c arefully to their request paying specific attention to the nature of the request. Calmly ask questions to extract the specifics of their request and why they’re requesting such help. Ask directed and detailed questions to learn whether the patient is imagining an unlikely or preventable future. Listen to the patient’s answers with sympathy but not as if you’re endorsing their request to their perception of what they consider to be a worthless life. The physician must be fully aware of his or her own biases in order to effectively respond to the patient’s needs. If the idea of suicide is offensive to the physician, the patient may feel his or her disapprobation and worry about abandonment.Step 2: Determine the Root CausesThe physician needs to assess the patient’s underlying causes for requesting physician-assisted suicide. The patient’s request may be a failure of the physician in addressing the needs of the patient. The attributes of suf fering should be focused on: physical, psychological, social, spiritual, and practical concerns. The physician should evaluate to see if the patient is having some type of clinical depression or common fear about their future outlook. The patient may be worrying about suffering with pain or other symptoms, loss of control or independence, a sense of abandonment, loneliness, indignity, a loss of their self-image, or being a burden to someone.Step 3: Affirm Your Commitment to Care for the PatientThe fear of abandonment is often felt in patients as they face the end-of-life. They want to be assured that someone will be with them at this time in their life. The physician should listen to and acknowledge the feelings and fears that the patient may express. They should commit to helping the patient find answers to their concerns. The physician should commit to the patient as well as the patient’s family and anyone who is close to the patient that they will continue to be the patien t’s physician until their life has ended.Step 4: Address the Root Causes of the RequestA patient’s request for a quick death is caused by some type of suffering on their behalf. They physician should discuss with the patient their health care preferences and goals. Alternative approaches or services should be discussed at this time with the patient. The physician should be able to determine if supportive counseling is needed for the patient.Step 5: Educate the Patient about Legal Alternatives for Control and ComfortPatients often have misconceptions about the benefits of requesting physician-assisted suicide. They may not be aware of the emotional effort that goes into planning for physician-assisted suicide. They also may not be aware of the emotional strain on family and friends. The physician should discuss the legal alternatives to physician-assisted suicide.The legal alternatives include refusal of treatment, withdrawal of treatment, declining oral intake, and end -of-life sedation. The patient should be made aware that they have a right to decline or consent to any treatment or hospitalization, but that their declining of treatment will not affect their ability to receive high quality end-of-life care. The patient should also be made aware that they have the right to stop any treatment at any time including the stopping of any fluids or nutrition.Patients suffering with unbearable and unmanageable pain may be approaching their last days or hours of life, and the only option available to them is end-of-life sedation. Before the end-of-life sedation should be considered for a patient, the attending physician and members of the health care team should know that all available therapies were tried. This option has to be agreed upon with the patient and their families with the patient have the final say so if they are capable of making the decision for themselves.Step 6: Consult with ColleaguesPhysician-assisted suicide requests are the most chall enging situations that physicians have to face in their practice of medicine. The physicians often hesitate to involve others in these situations for reasons about personal issues being raised, convictions about the inappropriateness of talking about death and concerns about the legal implications of the situation. The personal, ethical and legal ramifications for physician-assisted suicides should be supported by a trusted colleague or advisor of the physician. The trusted colleague could be a mentor, peer, religious advisor, or ethics consultants.Support may also come from nurses, social workers, chaplains, or other members involved in the care of the patient. Physician-assisted suicide requests should be a sign to the physician that a patient’s needs are not being met and that further evaluation is needed to identify the elements contributing to the patient’s suffering. Unfortunately, there is no easy answer to the question of physician-assisted suicide. Patients ha ve the right to withhold and withdraw life-sustaining procedures. Patients also have the right to receive powerful medication for pain relief and sedation. Physicians who oppose physician-assisted suicide do not always have to prescribe lethal medication.
Friday, January 3, 2020
Descartes Essay example - 757 Words
Descartes Is our education complete once a degree has been earned? Have we learned all there is to know? Can we be sure of what we have come to know? Only a completely self-assured person might answer yes to these questions, but for Rene Descartes (1596-1650) the completion of his formal education left him feeling and thinking he was still ignorant about the certainties of human experience and existence. This prominent Renaissance philosopher conquered the world of uncertainty in a work written in the 17th century. Mr. Descartes, Discourse on Method, quelled the skeptics with the assertion, I think, therefore I am. Most important to Descartes, however, was the method for which he was able to arrive at this axiom. The†¦show more content†¦Only know that which is clearly and distinctly to my mind. Second, to divide each difficulty I should examine into as many parts as possible. The third stage he set out to organize his thoughts into the easiest to the most complex, therefore, creating an orderly examination of the objects of knowledge. Finally, critical reviews of the links in [the] argument furthered his examination of the entire puzzle. Mr. Descartes methodology was paramount to the period in which it was born. However, its important to note that Descartes didnt think we could, as humans, understand all existence or phenomena. We cannot come to know Gods purposes. Mr. Descartes was optimistic of the fact that all men are capable of rational thought or reasoning. He took to a quiet environment and contemplated the serious problem for which he wanted to reconcile within himself; ho can man learn knowledge. Facilitating the process of reason is the element Descartes terms, the natural light of the mind. He argues that if we are to attain axiomatic truths we must be free of precipitancy and prejudice, whereby reason, the natural light of the mind, shall guide us to the certainties which define our existence. Descartes methodology was realized thro ugh his Metaphysical Doctrine, which asserted man and gods existence. In deep mediation the philosopher set out to deny everything which his senses told him. DescartesShow MoreRelatedDescartes Vs. Descartes Philosophy1142 Words  | 5 Pages Rene Descartes’ begins to illustrate his skeptical argument as presented in Meditation l. Descartes basic strategy to approaching this method of doubt is to defeat skepticism. This argument begins by doubting the truth of everything, from evidence of the senses to the fundamental process of reasoning. Therefore, if there is any truth in the world that overcomes the skeptical challenge then it must be indubitably true. Thus, creating a perfect foundation for knowledge. The first Meditation is anRead MoreHitchcock/Descartes924 Words  | 4 PagesHitchcock/Descartes Am I really awake typing a paper for philosophy? Did I just watch the Hitchcock film Shadow of a Doubt or did the â€Å"not so supremely good God†plant a reel of thoughts in my head (Descartes16)? That would be ironic since the themes of the film are based upon human understanding of doubt, dreams, good, evil, ignorance and knowledge. The film portrays a neat staircase that leads into the house of an all American family and a rickety set of stairs off the side of the house thatRead MoreAnalysis Of Rene Descartes s The Descartes 2020 Words  | 9 PagesRene Descartes was a French mathematician who concurred with Plato and the early scholars about the significance of reason. Nonetheless, he found that his antecedents regularly settled their thoughts upon what he took to be a to some degree temperamental and dubious establishment. 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His life was dedicated to the founding of a philosophical and mathematical system in which all sciences were logical. nbsp;nbsp;nbsp;nbsp;nbsp;Descartes was born in 1596 in Touraine, France. His education consisted of attendance to a Jesuit school of La Fleche. He studied a liberal arts program that emphasized philosophy, the humanities, science, and math. He then went on to the University of Poitiers whereRead MoreEssay on Descartes1128 Words  | 5 Pages Rene Descartes was one of the most influential thinkers in the history of the philosophy. Born in 1596, he lived to become a great mathematician, scientist, and philosopher. In fact, he became one of the central intellectual figures of the sixteen hundreds. He is believed by some to be the father of modern philosophy, although he was hampered by living in a time when other prominent scientists, such as Galileo, were persecuted for their discoveries and beliefs. Although this probably had an impactRead MoreDescartes vs. Locke1175 Words  | 5 PagesPhilosophy Essay (Descartes vs. Locke) Socrates once said, â€Å"As for me, all I know is that I know nothing.†Several philosophers contradicted Socrates’ outlook and believed that true knowledge was in fact attainable. This epistemological view however had several stances to it, as philosophers held different beliefs in regards to the derivation of true knowledge. Rationalists believed that the mind was the source of true knowledge, while in Empiricism, true knowledge derived from the senses. ReneRead MoreEssay on Renà © Descartes759 Words  | 4 PagesRenà © Descartes Renà © Descartes was a French philosopher and also mathematician. His method of doubt led him to the famous cogito ergo sum when translated means I am thinking, therefore I exist. This cogito was the foundation for Descartes quest for certain knowledge. He explored doubt and how we can prove our own existence, by taking the first steps of scepticism. His book Meditations On First Philosophy, was written in six parts. EachRead MoreObjections to Descartes’ Interactionism1431 Words  | 6 Pages In the following essay I will be offering some objections to Descartes’ interactionism as is primarily represented in his works The Passions of the Soul, Part I and Correspondence with Princess Elisabeth, Concerning the Union of Mind and Body. I will start by describing the basic features of how Descartes’ notion of interactionism works. Namely, that the pineal gland is the â€Å"principle seat†of the mind because it is the only singular part of the brain. The pineal gland also has a range ofRead More Rene Descartes Essay1094 Words  | 5 PagesRene Descartes was a famous French mathematician, scientist and philosopher. He was arguably the first major philosopher in the modern era to make a serious effort to defeat skepticism. His views about knowledge and certainty, as well as his views about the relationship between mind and body have been very influential over the last three centuries. Descartes was born at La Haye (now called Descartes), and educated at the Jesuit College of La Flà ¨che between 1606 and 1614. Descartes later claimed
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