What is the extreme f(x)=x^8e^x-7 ?

The extreme f(x)=x^8e^x-7 is Maximum(-8,(16777216)/(e^8)-7),Minimum(0,-7)

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extreme f(x)=x^8e^x-7

extreme points

f (x) = x^{8} e^{x} - 7

Maximum (- 8, \frac{16777216}{e ^{8}} - 7), Minimum (0, - 7)

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} - 7 : \frac{16777216}{e ^{8}} - 7

Maximum (- 8, \frac{16777216}{e ^{8}} - 7)

Plug

x = 0

into

x^{8} e^{x} - 7 : - 7

Minimum (0, - 7)

Maximum (- 8, \frac{16777216}{e ^{8}} - 7), Minimum (0, - 7)

What is the extreme f(x)=x^8e^x-7 ?
The extreme f(x)=x^8e^x-7 is Maximum(-8,(16777216)/(e^8)-7),Minimum(0,-7)