en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme f(x)=(x^2-1/2)e^{-2x}

Solution

extreme

Solution

Minimum (\frac{1 - 3}{2}, \frac{e ^{- 1 + 3} ( 1 - 3 )}{2}), Maximum (\frac{1 + 3}{2}, \frac{e ^{- 1 - 3} ( 1 + 3 )}{2})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < \frac{- 3 + 1}{2},

Increasing

: \frac{- 3 + 1}{2} < x < \frac{1 + 3}{2},

Decreasing

: \frac{1 + 3}{2} < x < \infty

Plug

x = \frac{1 - 3}{2}

into

(x^{2} - \frac{1}{2}) e^{- 2 x} : \frac{e ^{- 1 + 3} ( 1 - 3 )}{2}

Minimum (\frac{1 - 3}{2}, \frac{e ^{- 1 + 3} ( 1 - 3 )}{2})

Plug

x = \frac{1 + 3}{2}

into

(x^{2} - \frac{1}{2}) e^{- 2 x} : \frac{e ^{- 1 - 3} ( 1 + 3 )}{2}

Maximum (\frac{1 + 3}{2}, \frac{e ^{- 1 - 3} ( 1 + 3 )}{2})

Minimum (\frac{1 - 3}{2}, \frac{e ^{- 1 + 3} ( 1 - 3 )}{2}), Maximum (\frac{1 + 3}{2}, \frac{e ^{- 1 - 3} ( 1 + 3 )}{2})

Graph

Popular Examples

extreme f(x)=x^2+y^2-16=0

extreme 2x^2-2x^2y+y^2

extreme x^2+x+2

extreme (x-5)/(x^2-18x+81)

extreme f(x,y)=x^3y^2+2xy-5

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^2-1/2)e^{-2x} ?
The extreme f(x)=(x^2-1/2)e^{-2x} is