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Popular >

extreme x/(x^2+25)

Solution

extreme points

\frac{x}{x ^{2} + 25}

Solution

Minimum (- 5, - \frac{1}{10}), Maximum (5, \frac{1}{10})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 25}{( x ^{2} + 25 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 5

into

\frac{x}{x ^{2} + 25} : - \frac{1}{10}

Minimum (- 5, - \frac{1}{10})

Plug

x = 5

into

\frac{x}{x ^{2} + 25} : \frac{1}{10}

Maximum (5, \frac{1}{10})

Minimum (- 5, - \frac{1}{10}), Maximum (5, \frac{1}{10})

Popular Examples

domain of 1/(x^2-3x+2)domain

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

inverse of f(x)=x^3-2 inverse

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

critical f(x)=(40t)/(t^2+25)critical points

f (x) = \frac{40 t}{t ^{2} + 25}

asymptotes of (2x^2-4)/(x+3)asymptotes

\frac{2 x ^{2} - 4}{x + 3}

asymptotes of 5/(x^2-9)asymptotes

\frac{5}{x ^{2} - 9}

Frequently Asked Questions (FAQ)

What is the extreme x/(x^2+25) ?
The extreme x/(x^2+25) is Minimum(-5,-1/10),Maximum(5, 1/10)