calculus

Find all relative extreme points y=x e^-x

  1. 👍 0
  2. 👎 0
  3. 👁 177
  1. Find the definition of a relative extreme point, for example:
    http://en.wikipedia.org/wiki/Extreme_point

    hint:
    1. find the domain of the function
    f(x)=x*e^(-x)
    ...the domain is (-∞,∞)
    2. calculate f'(x), and verify that f'(x) exists within the domain.
    3. find the zeroes of f'(x)=0
    4. check that the zeroes found in (3) are maxima or minima by evaluating f"(x).
    If f"(x)=0, it is an inflection point and is not an extremum, thus not a critical point.

    There should be one relative extreme point for the given function on its domain.

    1. 👍 0
    2. 👎 0
  2. I still can't find the answer because I got max (1,1/e)

    1. 👍 0
    2. 👎 0
  3. I had the impression that the question was looking for relative extreme values in calculus, in which case (1,1/e) is the answer. The function tends to -∞ as x-> -∞ and f(x)->0 as x->∞, and is a maximum at x=1 (when y=1/e).

    I am sorry that the reference for extreme point in the Wiki article does not refer to the same subject.
    Can you check if the following link refers to what you are working on in class?

    http://en.wikibooks.org/wiki/Calculus/Extreme_Value_Theorem

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Find and classify all the extreme points for the f unction f(x,y) =𝑥^2 +𝑦^2 -xy+x.

    asked by Anonymous on July 11, 2020
  2. english

    the Trout" and "The Wager," Below is a chart which shows the continuum from Pessimistic to Optimistic and on which you can "gauge" where a character fits at each point in the story. For each of the stories, "The Trout" and "The

    asked by sherrie on June 1, 2013
  3. Derivative Test

    Consider the function y = 3x5 – 25x3 + 60x + 1. Use the first or second derivative test to test the critical points. How many relative maxima did you find? I got 2 as the relative maxima, is this done correctly?

    asked by May on December 9, 2014
  4. Calculus

    Find the values of x that give relative extrema for the function f(x)=3x^5-5x^3 A. Relative maximum: x= 1; Relative minimum: x=sqrt(5/3) B. Relative maximum: x=-1; Relative minimum: x=1 C. Relative maxima: x=+or- 1; Relative

    asked by Anonymous on January 11, 2015
  5. CAL

    Consider the function y = 3x^5 – 25x^3 + 60x + 1 Use the first or second derivative test to test the critical points. How many relative maxima did you find? I got this as the derivative; 15 (4-5 x^2+x^4) And I got 4 relative

    asked by Jamie on January 9, 2015
  1. differentiability

    If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f prime of x equals (x2-4)*g(x), which of the following is true? A. f has a relative maximum at x=-2 and a relative minimum at x=2, B. f

    asked by matthew on December 31, 2010
  2. geometry CA

    Graph quadrilateral ABCD. Then determine the most precise name for each quadrilateral. 1. A (0, 5), B (–5, 0), C (0, –5), D (5, 0) (1 point) square kite rectangle 2. A (–4, 4), B (3, 4), C (5, 0), D (–2, 0) (1 point)

    asked by Jesicca on March 11, 2011
  3. Calculus

    Find the relative extrema, if any, of the function. Use the second derivative test, if applicable. (If an answer does not exist, enter DNE.) f(t) = 7 t + 3/t relative maximum (x, y) = relative minimum (x, y) =

    asked by Anonymous on June 18, 2013
  4. Algebra 2

    Please help super confused!!! Which points are the best approximation of the relative maximum and minimum of the function? f(x)=x^3+3x^2-9x-8 a. Relative max is at (3,-13), relative min is at (-3,-19). b. Relative max is at

    asked by Olivia N J on November 14, 2016
  5. calculus

    Find all relative extrema and points of inflection of the function: f(x) = sin (x/2) 0 =< x =< 4pi =< is supposed to be less than or equal to. I can find the extrema, but the points of inflection has me stumped. The inflection

    asked by James on November 14, 2010
  6. Math

    Find the intervals on which the function is increasing, decreasing, concave up, or concave down and find any local extreme values and inflection points. So I know how to do the above, but not with piece wise functions. Someone

    asked by Beth on February 3, 2016

You can view more similar questions or ask a new question.