en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme y= x/(1+x^2)

Solution

extreme points

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

Solution

Minimum (- 1, - \frac{1}{2}), Maximum (1, \frac{1}{2})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

\frac{x}{1 + x ^{2}} : - \frac{1}{2}

Minimum (- 1, - \frac{1}{2})

Plug

x = 1

into

\frac{x}{1 + x ^{2}} : \frac{1}{2}

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

Minimum (- 1, - \frac{1}{2}), Maximum (1, \frac{1}{2})

Popular Examples

extreme (x^2-1)/(x^2-4)extreme points

\frac{x ^{2} - 1}{x ^{2} - 4}

extreme f(x)=5x^2ln(x)extreme points

f (x) = 5 x^{2} ln (x)

extreme f(x,y)=2x^2+8xy+y^4 extreme points

f (x, y) = 2 x^{2} + 8 x y + y^{4}

extreme f(x)=2x^3+9x^2+1 extreme points

f (x) = 2 x^{3} + 9 x^{2} + 1

F (m, a) = m \cdot a

Frequently Asked Questions (FAQ)

What is the extreme y= x/(1+x^2) ?
The extreme y= x/(1+x^2) is Minimum(-1,-1/2),Maximum(1, 1/2)