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Popular >

extreme f(x)= x/(x^2+2)

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

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

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

Plug

x = 2

into

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

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

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

Popular Examples

line (-2,1),(-8,4)line

(- 2, 1), (- 8, 4)

inverse of f(x)=-2/3 x+6 inverse

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

asymptotes of f(x)=(4x+9)/(3x-2)asymptotes

f (x) = \frac{4 x + 9}{3 x - 2}

(- 8) 1

line (4,48),(-3,27)line

(4, 48), (- 3, 27)

Frequently Asked Questions (FAQ)

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