en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme (x^3)/(e^x)

Solution

extreme points

\frac{x ^{3}}{e ^{x}}

Solution

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

\frac{x ^{3}}{e ^{x}} : 0

Saddle (0, 0)

Plug

x = 3

into

\frac{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

extreme x+(33)/x extreme points

x + \frac{33}{x}

extreme y= 1/3 x^3-x^2+2x extreme points

y = \frac{1}{3} x^{3} - x^{2} + 2 x

extreme f(x)=4xsqrt(1-5x)extreme points

f (x) = 4 x 1 - 5 x

extreme f(x)=x^3-3xy-y^2 extreme points

f (x) = x^{3} - 3 x y - y^{2}

extreme f(x)=f(x)=3x^4-8x^3-6x^2+24x-3 extreme points

f (x) = f (x) = 3 x^{4} - 8 x^{3} - 6 x^{2} + 24 x - 3

Frequently Asked Questions (FAQ)

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