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

The extreme f(x)=x^2*e^{-x^2} is Maximum(-1, 1/e),Minimum(0,0),Maximum(1, 1/e)

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

extreme

Maximum (- 1, \frac{1}{e}), Minimum (0, 0), Maximum (1, \frac{1}{e})

Solution steps

f^{'} (x) = - 2 e^{- x^{2}} x (x + 1) (x - 1)

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

x^{2} \cdot e^{- x^{2}} : \frac{1}{e}

Maximum (- 1, \frac{1}{e})

Plug

x = 0

into

x^{2} \cdot e^{- x^{2}} : 0

Minimum (0, 0)

Plug

x = 1

into

x^{2} \cdot e^{- x^{2}} : \frac{1}{e}

Maximum (1, \frac{1}{e})

Maximum (- 1, \frac{1}{e}), Minimum (0, 0), Maximum (1, \frac{1}{e})

What is the extreme f(x)=x^2*e^{-x^2} ?
The extreme f(x)=x^2*e^{-x^2} is Maximum(-1, 1/e),Minimum(0,0),Maximum(1, 1/e)