en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme x^2e^{-x}

Solution

extreme points

x^{2} e^{- x}

Solution

Minimum (0, 0), Maximum (2, \frac{4}{e ^{2}})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 2

into

x^{2} e^{- x} : \frac{4}{e ^{2}}

Maximum (2, \frac{4}{e ^{2}})

Minimum (0, 0), Maximum (2, \frac{4}{e ^{2}})

Graph

Popular Examples

inverse of f(x)=(3x+2)/7

intercepts of 2/7

inverse of 2x^2-8x

inverse of f(x)=-x^3

intercepts of f(x)=\sqrt[3]{x-2}

Frequently Asked Questions (FAQ)

What is the extreme x^2e^{-x} ?
The extreme x^2e^{-x} is Minimum(0,0),Maximum(2, 4/(e^2))