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…)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

extreme

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)

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…)