What is the extreme f(x)=x^6e^x-3 ?

The extreme f(x)=x^6e^x-3 is Maximum(-6,(46656)/(e^6)-3),Minimum(0,-3)

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extreme f(x)=x^6e^x-3

extreme points

f (x) = x^{6} e^{x} - 3

Maximum (- 6, \frac{46656}{e ^{6}} - 3), Minimum (0, - 3)

Solution steps

f^{'} (x) = e^{x} x^{6} + 6 e^{x} x^{5}

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

x^{6} e^{x} - 3 : \frac{46656}{e ^{6}} - 3

Maximum (- 6, \frac{46656}{e ^{6}} - 3)

Plug

x = 0

into

x^{6} e^{x} - 3 : - 3

Minimum (0, - 3)

Maximum (- 6, \frac{46656}{e ^{6}} - 3), Minimum (0, - 3)

What is the extreme f(x)=x^6e^x-3 ?
The extreme f(x)=x^6e^x-3 is Maximum(-6,(46656)/(e^6)-3),Minimum(0,-3)