What is the extreme f(x)=(x^5)/(e^{4x)} ?

The extreme f(x)=(x^5)/(e^{4x)} is Saddle(0,0),Maximum(5/4 ,(3125)/(1024e^5))

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extreme f(x)=(x^5)/(e^{4x)}

extreme

Saddle (0, 0), Maximum (\frac{5}{4}, \frac{3125}{1024 e ^{5}})

Solution steps

f^{'} (x) = \frac{x ^{4} ( 5 - 4 x )}{e ^{4 x}}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{5}{4},

Decreasing

: \frac{5}{4} < x < \infty

Plug

x = 0

into

\frac{x ^{5}}{e ^{4 x}} : 0

Saddle (0, 0)

Plug

x = \frac{5}{4}

into

\frac{x ^{5}}{e ^{4 x}} : \frac{3125}{1024 e ^{5}}

Maximum (\frac{5}{4}, \frac{3125}{1024 e ^{5}})

Saddle (0, 0), Maximum (\frac{5}{4}, \frac{3125}{1024 e ^{5}})

What is the extreme f(x)=(x^5)/(e^{4x)} ?
The extreme f(x)=(x^5)/(e^{4x)} is Saddle(0,0),Maximum(5/4 ,(3125)/(1024e^5))