Calculus

posted by .

Find the indicated absolute extremum as well as all values of x where it occurs on the specified domain

f(x)= x^2e^-0.25x ; [3,10]

  • Calculus -

    Find f'(x) and see if there is a zero (root) on the interval.

    If not, the extrema are the two limits of the interval.

    Check the sign of f'(x) on the interval. If there is no zero on the interval, the sign should not change (+ OR -).

    If f'(x) is + on the interval, it is monotonically increasing, and vice versa.

    If it is monotonically increasing or decreasing, then f(c1) and f(c1) are the limits of the range of the function on the given interval [c1,c2]. I.e. the function does not take up values beyond [f(c1),f(c2)].

    Post your answer for checking if you wish.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    f(x)=xe^(-2x) with domain 0< or equal to x< or equal to 10 find all values of x for which the graph of f is increasing and all values of x for which the graph is decreasing give the x and y coordinates if all absolute max and …
  2. Calculus (pleas help!!!)

    Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum …
  3. Calculus (pleas help!!!)

    Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum …
  4. Calculus

    Find the value of the derivative at each indicated extremum.
  5. Calculus

    Find the absolute maximum and absolute minimum values of the function f(x)=x^3+6x^2-63x+4 on each of the indicated variables. Enter DNE for does not exist. (A) Interval = [-8,0] Absolute maximum = Absolute minimum = (B) Interval = …
  6. calculus

    2) Let g(s)= t(4−t)^1/2 on the interval [0,2]. Find the absolute maximum and absolute minimum of g(t) on this interval. Enter DNE if the absolute maximum or minimum does not exist. The absolute max occurs at t= . The absolute …
  7. calculus

    Let f(x)=-x^2+3x on the interval [1,3]. Find the absolute maximum and absolute minimum of f(x) on this interval. The absolute max occurs at x=. The absolute min occurs at x=
  8. calculus

    Let g(s)=1/(s-2) on the interval [0,1]. Find the absolute maximum and absolute minimum of g(s) on this interval. The absolute max occurs at s=. The absolute min occurs at s=
  9. Calculus

    Let f(t)=t\sqrt{4-t} on the interval [-1,3]. Find the absolute maximum and absolute minimum of f(t) on this interval. The absolute max occurs at t=. The absolute min occurs at t=
  10. calculus

    Let g(x)=(4x)/(x^2+1) on the interval [-4,0]. Find the absolute maximum and absolute minimum of g(x) on this interval. The absolute max occurs at x=. The absolute min occurs at x=

More Similar Questions