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Popular >

extreme x/(x^2+1)

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

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

Plug

x = 1

into

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

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

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

Popular Examples

slope of y=-3/2 x slope

y = - \frac{3}{2} x

domain of f(x)=1-2x-x^2 domain

f (x) = 1 - 2 x - x^{2}

inflection x^2+2x+3 inflection points

x^{2} + 2 x + 3

inverse of f(x)=(x-5)/2 inverse

f (x) = \frac{x - 5}{2}

domain of |x|-2 domain

∣ x ∣ - 2

Frequently Asked Questions (FAQ)

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