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}

Solution

extreme points

x^{3} e^{- x}

Solution

Saddle (0, 0), Maximum (3, \frac{27}{e ^{3}})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 3

into

x^{3} e^{- x} : \frac{27}{e ^{3}}

Maximum (3, \frac{27}{e ^{3}})

Saddle (0, 0), Maximum (3, \frac{27}{e ^{3}})

Popular Examples

simplify (4ef^2)^2(4ef^2)^2 simplify

(4 e f^{2})^{2} (4 e f^{2})^{2}

simplify 8*e^{-2}simplify

8 \cdot e^{- 2}

simplify (-0.4)^{-n}z^n simplify

(- 0.4)^{- n} z^{n}

simplify (sqrt(2))/(sqrt(51))simplify

\frac{2}{51}

simplify (0.3(2+(2-1)^2))0.6*0.3 simplify

(0.3 (2 + (2 - 1)^{2})) 0.6 \cdot 0.3

Frequently Asked Questions (FAQ)

What is the extreme x^3e^{-x} ?
The extreme x^3e^{-x} is Saddle(0,0),Maximum(3,(27)/(e^3))