Question

Determine the location and values of the absolute maximum and absolute minimum for the given function
F(x)=(-x+2)4,

Answer 1

Answer:

By the Extreme Value Theorem, the function is continuous on the interval and hence could have maximum and minimum at the end points. Moreover, the function is differentible on the open interval, so the extreme values can occur either at the end points of [−2,8] or when f′(x)=0.

f′(x)=2xe−x2−12x2e−x2=0⇒4x−x2=0⇒(x=0)or(x=4)

Hence, now you have four points to be checked:

x=0 and x=4

x=−2 and x=8

The rest is easy.

Answer 2

Answer:

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