en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^3e^{-x^2}

Solution

extreme points

x^{3} e^{- x^{2}}

Solution

Minimum (- \frac{3}{2}, - \frac{3 3}{2 2 e ^{\frac{3}{2}}}), Saddle (0, 0), Maximum (\frac{3}{2}, \frac{3 3}{2 2 e ^{\frac{3}{2}}})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - \frac{3}{2},

Increasing

: - \frac{3}{2} < x < 0,

Increasing

: 0 < x < \frac{3}{2},

Decreasing

: \frac{3}{2} < x < \infty

Plug

x = - \frac{3}{2}

into

x^{3} e^{- x^{2}} : - \frac{3 3}{2 2 e ^{\frac{3}{2}}}

Minimum (- \frac{3}{2}, - \frac{3 3}{2 2 e ^{\frac{3}{2}}})

Plug

x = 0

into

x^{3} e^{- x^{2}} : 0

Saddle (0, 0)

Plug

x = \frac{3}{2}

into

x^{3} e^{- x^{2}} : \frac{3 3}{2 2 e ^{\frac{3}{2}}}

Maximum (\frac{3}{2}, \frac{3 3}{2 2 e ^{\frac{3}{2}}})

Minimum (- \frac{3}{2}, - \frac{3 3}{2 2 e ^{\frac{3}{2}}}), Saddle (0, 0), Maximum (\frac{3}{2}, \frac{3 3}{2 2 e ^{\frac{3}{2}}})

Popular Examples

simplify \sqrt[30]{3^{12}}simplify

simplify 195e^{(-0.173*365)}simplify

195 e^{(- 0.173 \cdot 365)}

simplify \sqrt[4]{X^Z}simplify

simplify 200(1-e^{-1})(2e^{-2(400)})simplify

200 (1 - e^{- 1}) (2 e^{- 2 (400)})

simplify (4sqrt(3))(6sqrt(10))simplify

(43) (610)

Frequently Asked Questions (FAQ)

What is the extreme x^3e^{-x^2} ?
The extreme x^3e^{-x^2} is