What is the extreme f(x)=x^6e^x-7 ?

The extreme f(x)=x^6e^x-7 is Maximum(-6,(46656)/(e^6)-7),Minimum(0,-7)

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extreme f(x)=x^6e^x-7

extreme points

f (x) = x^{6} e^{x} - 7

Maximum (- 6, \frac{46656}{e ^{6}} - 7), Minimum (0, - 7)

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} - 7 : \frac{46656}{e ^{6}} - 7

Maximum (- 6, \frac{46656}{e ^{6}} - 7)

Plug

x = 0

into

x^{6} e^{x} - 7 : - 7

Minimum (0, - 7)

Maximum (- 6, \frac{46656}{e ^{6}} - 7), Minimum (0, - 7)

f (x) = lo g_{2} (\frac{e ^{x} - 6}{4})

(- 2, - 8), (2, - 3)

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

(y - 3)^{2} = 8 (x - 5)

f (x) = \frac{x ^{2} + 6 x + 9}{x ^{3} + 7 x ^{2}}

What is the extreme f(x)=x^6e^x-7 ?
The extreme f(x)=x^6e^x-7 is Maximum(-6,(46656)/(e^6)-7),Minimum(0,-7)