What is the extreme f(x)=((x^9))/(e^{2x)} ?

The extreme f(x)=((x^9))/(e^{2x)} is Saddle(0,0),Maximum(9/2 ,(387420489)/(512e^9))

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extreme f(x)=((x^9))/(e^{2x)}

extreme points

f (x) = \frac{( x ^{9} )}{e ^{2 x}}

Saddle (0, 0), Maximum (\frac{9}{2}, \frac{387420489}{512 e ^{9}})

Solution steps

f^{'} (x) = \frac{x ^{8} ( 9 - 2 x )}{e ^{2 x}}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{9}{2},

Decreasing

: \frac{9}{2} < x < \infty

Plug

x = 0

into

\frac{x ^{9}}{e ^{2 x}} : 0

Saddle (0, 0)

Plug

x = \frac{9}{2}

into

\frac{x ^{9}}{e ^{2 x}} : \frac{387420489}{512 e ^{9}}

Maximum (\frac{9}{2}, \frac{387420489}{512 e ^{9}})

Saddle (0, 0), Maximum (\frac{9}{2}, \frac{387420489}{512 e ^{9}})

f (x, y) = x^{2} - y^{2} + 21

- \frac{5 e ^{4 x}}{x - 4}

f (x, y) = x - k y

f (x) = \frac{x + 3}{x ^{2} - 2 x - 15}

f (x) = x^{2} (e^{- x^{2}})

What is the extreme f(x)=((x^9))/(e^{2x)} ?
The extreme f(x)=((x^9))/(e^{2x)} is Saddle(0,0),Maximum(9/2 ,(387420489)/(512e^9))