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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Minimum (0, 0), Maximum (\frac{1}{2}, \frac{2}{e})

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Plug

x = 0

into

2 x e^{- x} : 0

Minimum (0, 0)

Plug

x = \frac{1}{2}

into

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

Maximum (\frac{1}{2}, \frac{2}{e})

Minimum (0, 0), Maximum (\frac{1}{2}, \frac{2}{e})

f (x) = - x^{4} + 50 x^{2} - 625, - 6 \leq x \leq 6

f (x) = \frac{x ^{2}}{x + 2}

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

f (x) = x^{2} - 12 x - 13

f (x) = 15 x^{\frac{2}{3}} - 10 x

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