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Popular >

extreme e^x(8-x^2)

Solution

extreme points

e^{x} (8 - x^{2})

Solution

Minimum (- 4, - \frac{8}{e ^{4}}), Maximum (2, 4 e^{2})

Solution steps

f^{'} (x) = - e^{x} (x - 2) (x + 4)

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 4

into

e^{x} (8 - x^{2}) : - \frac{8}{e ^{4}}

Minimum (- 4, - \frac{8}{e ^{4}})

Plug

x = 2

into

e^{x} (8 - x^{2}) : 4 e^{2}

Maximum (2, 4 e^{2})

Minimum (- 4, - \frac{8}{e ^{4}}), Maximum (2, 4 e^{2})

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Frequently Asked Questions (FAQ)

What is the extreme e^x(8-x^2) ?
The extreme e^x(8-x^2) is Minimum(-4,-8/(e^4)),Maximum(2,4e^2)