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Popular >

extreme (x^2-8)e^x

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 4

into

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

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

Plug

x = 2

into

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

Minimum (2, - 4 e^{2})

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

Popular Examples

inverse of f(x)=sqrt(x+2)+1 inverse

f (x) = x + 2 + 1

inverse of f(x)= 1/2 x^{3/2}inverse

f (x) = \frac{1}{2} x^{\frac{3}{2}}

range of f(x)=(x+1)^2 range

f (x) = (x + 1)^{2}

distance (0,-3),(6,3)distance

(0, - 3), (6, 3)

domain of f(x)=ln(x-x^2)domain

f (x) = ln (x - x^{2})

Frequently Asked Questions (FAQ)

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