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Popular >

extreme (4x)/(x^2+9)

Solution

extreme points

\frac{4 x}{x ^{2} + 9}

Solution

Minimum (- 3, - \frac{2}{3}), Maximum (3, \frac{2}{3})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

\frac{4 x}{x ^{2} + 9} : - \frac{2}{3}

Minimum (- 3, - \frac{2}{3})

Plug

x = 3

into

\frac{4 x}{x ^{2} + 9} : \frac{2}{3}

Maximum (3, \frac{2}{3})

Minimum (- 3, - \frac{2}{3}), Maximum (3, \frac{2}{3})

Popular Examples

inverse of y=9x inverse

y = 9 x

inverse of f(x)=(-1)/(4(x-6))inverse

f (x) = \frac{- 1}{4 ( x - 6 )}

midpoint (-1,1),(5,-5)midpoint

(- 1, 1), (5, - 5)

domain of g(x)=(1/2)^{x-1}domain

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

critical f(x)=x^2-2 critical points

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

Frequently Asked Questions (FAQ)

What is the extreme (4x)/(x^2+9) ?
The extreme (4x)/(x^2+9) is Minimum(-3,-2/3),Maximum(3, 2/3)