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

The extreme f(x)=x^2e^{-9x} is Minimum(0,0),Maximum(2/9 , 4/(81e^2))

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

extreme points

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

Minimum (0, 0), Maximum (\frac{2}{9}, \frac{4}{81 e ^{2}})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

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

Decreasing

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

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{2}{9}

into

x^{2} e^{- 9 x} : \frac{4}{81 e ^{2}}

Maximum (\frac{2}{9}, \frac{4}{81 e ^{2}})

Minimum (0, 0), Maximum (\frac{2}{9}, \frac{4}{81 e ^{2}})

f (x, y) = x y - x^{2} - y^{2} - 2 x - 2 y + 4

y = \frac{ln ( x )}{x}

x^{2} + y^{2} + x^{2} y + 4

f (x) = 4 x^{5} - 8 x^{4} - 5 x^{3} + 10 x^{2} + x - 2

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

What is the extreme f(x)=x^2e^{-9x} ?
The extreme f(x)=x^2e^{-9x} is Minimum(0,0),Maximum(2/9 , 4/(81e^2))