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Popular >

extreme x/(1+x^2)

Solution

extreme points

\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 f(x)=x^3-5x^2+3x+10 extreme points

f (x) = x^{3} - 5 x^{2} + 3 x + 10

extreme f(x)=e^{-x}extreme points

f (x) = e^{- x}

extreme f(x)=9x^{2/3}+3x-6 extreme points

f (x) = 9 x^{\frac{2}{3}} + 3 x - 6

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

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

extreme f(x)=(x^2-2x+2)/(x-1)extreme points

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

Frequently Asked Questions (FAQ)

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