What is the extreme f(x)=x^2e^{-0.1x} ?

The extreme f(x)=x^2e^{-0.1x} is Minimum(0,0),Maximum(20,(400)/(e^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x^2e^{-0.1x}

extreme points

f (x) = x^{2} e^{- 0.1 x}

Minimum (0, 0), Maximum (20, \frac{400}{e ^{2}})

Solution steps

f^{'} (x) = e^{- 0.1 x} x (2 - 0.1 x)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 20,

Decreasing

: 20 < x < \infty

Plug

x = 0

into

x^{2} e^{- 0.1 x} : 0

Minimum (0, 0)

Plug

x = 20

into

x^{2} e^{- 0.1 x} : \frac{400}{e ^{2}}

Maximum (20, \frac{400}{e ^{2}})

Minimum (0, 0), Maximum (20, \frac{400}{e ^{2}})

f (x) = x - 1 + \frac{4}{x ^{2} - 4}

2 x - 5

(5, 6), (4, 1)

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

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

What is the extreme f(x)=x^2e^{-0.1x} ?
The extreme f(x)=x^2e^{-0.1x} is Minimum(0,0),Maximum(20,(400)/(e^2))