Absolute maxima and minima Determine the location and value of

Reginald Metcalf

Reginald Metcalf

Answered question

2021-12-09

Absolute maxima and minima Determine the location and value of the absolute extreme value of ƒ on the given interval, if they exist.
f(x)=2exx2 on [0,2e]

Answer & Explanation

Buck Henry

Buck Henry

Beginner2021-12-10Added 33 answers

Step 1
Given f(x)=2exx2,x[0,2e].
The absolute maxima and minima if exist is located on the critical points or at the end points of the interval.
Compute the critical points as follows:
f'(x)=0
2exx2=0
2e-2x=0
x=e
Step 2
Now compute the value of f at x=e,0,2e as follows:
f(e)=2e22e2=0
f(0)=0-0=0
f(2e)=4e22e2=2e2
Therefore, the absolute maximum of f occurs at x=2e and the maximum value is 2e2.
The absolute minimum of f occurs at x=0, e and the minimum value is 0.

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