What is the extreme f(x)=x^2e^{-0.1x} ?

The extreme f(x)=x^2e^{-0.1x} is Minimum(0,0),Maximum(20,(400)/(e^2))

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extreme f(x)=x^2e^{-0.1x}

extreme

Minimum (0, 0), Maximum (20, \frac{400}{e ^{2}})

Solution steps

f^{'} (x) = e^{- 0.1 x} x (2 - 0.1 x)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 20,

Decreasing

: 20 < x < \infty

Plug

x = 0

into

x^{2} e^{- 0.1 x} : 0

Minimum (0, 0)

Plug

x = 20

into

x^{2} e^{- 0.1 x} : \frac{400}{e ^{2}}

Maximum (20, \frac{400}{e ^{2}})

Minimum (0, 0), Maximum (20, \frac{400}{e ^{2}})

What is the extreme f(x)=x^2e^{-0.1x} ?
The extreme f(x)=x^2e^{-0.1x} is Minimum(0,0),Maximum(20,(400)/(e^2))