What is the extreme f(x)=x^8e^x-8 ?

The extreme f(x)=x^8e^x-8 is Maximum(-8,(16777216)/(e^8)-8),Minimum(0,-8)

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extreme f(x)=x^8e^x-8

extreme points

f (x) = x^{8} e^{x} - 8

Maximum (- 8, \frac{16777216}{e ^{8}} - 8), Minimum (0, - 8)

Solution steps

f^{'} (x) = e^{x} x^{8} + 8 e^{x} x^{7}

Find intervals:

Increasing

: - \infty < x < - 8,

Decreasing

: - 8 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 8

into

x^{8} e^{x} - 8 : \frac{16777216}{e ^{8}} - 8

Maximum (- 8, \frac{16777216}{e ^{8}} - 8)

Plug

x = 0

into

x^{8} e^{x} - 8 : - 8

Minimum (0, - 8)

Maximum (- 8, \frac{16777216}{e ^{8}} - 8), Minimum (0, - 8)

in v erse f (x) = e^{2 x + 6}

l in e (1, - 1), (0, 2)

in v erse f (x) = \frac{2}{x - 5}

d o main \frac{x - 6}{x - 7}

in t erce pt s y = - x^{8} + 8 x + 1

What is the extreme f(x)=x^8e^x-8 ?
The extreme f(x)=x^8e^x-8 is Maximum(-8,(16777216)/(e^8)-8),Minimum(0,-8)