What is the extreme f(x)=xe^{-x^2}[0.2] ?

The extreme f(x)=xe^{-x^2}[0.2] is Minimum(-1/(sqrt(2)),-0.08577…),Maximum(1/(sqrt(2)),0.08577…)

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extreme f(x)=xe^{-x^2}[0.2]

extreme points

f (x) = x e^{- x^{2}} [0.2]

Minimum (- \frac{1}{2}, - 0.08577 \dots), Maximum (\frac{1}{2}, 0.08577 \dots)

Solution steps

Find the critical points:

x = - \frac{1}{2}, x = \frac{1}{2}

Domain of

x e^{- x^{2}} [0.2] : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{2},

Increasing

: - \frac{1}{2} < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < \infty

Plug the extreme point

x = - \frac{1}{2}

into

x e^{- x^{2}} [0.2] \Rightarrow y = - 0.08577 \dots

Minimum (- \frac{1}{2}, - 0.08577 \dots)

Plug the extreme point

x = \frac{1}{2}

into

x e^{- x^{2}} [0.2] \Rightarrow y = 0.08577 \dots

Maximum (\frac{1}{2}, 0.08577 \dots)

Minimum (- \frac{1}{2}, - 0.08577 \dots), Maximum (\frac{1}{2}, 0.08577 \dots)

f (x) = - 2 x^{3} + 30 x^{2} - 54 x + 6

f (x) = - 2 x^{3} + 30 x^{2} - 54 x + 8

- 6 x + x^{2}

f (x, y) = 6 x - 8 y + 7 x y

f (x) = - x^{3} + 3 x^{2} - 9

What is the extreme f(x)=xe^{-x^2}[0.2] ?
The extreme f(x)=xe^{-x^2}[0.2] is Minimum(-1/(sqrt(2)),-0.08577…),Maximum(1/(sqrt(2)),0.08577…)