What is the extreme f(x)=(x^8)/(e^{7x)} ?

The extreme f(x)=(x^8)/(e^{7x)} is Minimum(0,0),Maximum(8/7 ,(16777216)/(5764801e^8))

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extreme f(x)=(x^8)/(e^{7x)}

extreme

Minimum (0, 0), Maximum (\frac{8}{7}, \frac{16777216}{5764801 e ^{8}})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{8}{7},

Decreasing

: \frac{8}{7} < x < \infty

Plug

x = 0

into

\frac{x ^{8}}{e ^{7 x}} : 0

Minimum (0, 0)

Plug

x = \frac{8}{7}

into

\frac{x ^{8}}{e ^{7 x}} : \frac{16777216}{5764801 e ^{8}}

Maximum (\frac{8}{7}, \frac{16777216}{5764801 e ^{8}})

Minimum (0, 0), Maximum (\frac{8}{7}, \frac{16777216}{5764801 e ^{8}})

What is the extreme f(x)=(x^8)/(e^{7x)} ?
The extreme f(x)=(x^8)/(e^{7x)} is Minimum(0,0),Maximum(8/7 ,(16777216)/(5764801e^8))