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

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

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

extreme points

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

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

Solution steps

f^{'} (x) = 9 x^{8} e^{2 x} + e^{2 x} \cdot 2 x^{9}

Find intervals:

Decreasing

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

Increasing

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

Increasing

: 0 < x < \infty

Plug

x = - \frac{9}{2}

into

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

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

Plug

x = 0

into

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

Saddle (0, 0)

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

f (x) = x (18 - 40 + 2 x) (\frac{40}{2} - x)

f (x) = 0.001 x^{2} + 3.8 x - 70

f (x) = x^{3} - 27 x + 51

f (x) = x^{3} - 27 x + 50

g (x) = x^{3} - 3 x + 2

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