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Popular Functions >

extreme y= x/(x^2+9)

Solution

extreme points

y = \frac{x}{x ^{2} + 9}

Solution

Minimum (- 3, - \frac{1}{6}), Maximum (3, \frac{1}{6})

Solution steps

f^{'} (x) = \frac{- 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{x}{x ^{2} + 9} : - \frac{1}{6}

Minimum (- 3, - \frac{1}{6})

Plug

x = 3

into

\frac{x}{x ^{2} + 9} : \frac{1}{6}

Maximum (3, \frac{1}{6})

Minimum (- 3, - \frac{1}{6}), Maximum (3, \frac{1}{6})

Graph

Popular Examples

extreme f(x)=x^2-4,-3<= x<= 2

extreme f(x)=(7.8x^2-225x+1709)

extreme f(x)=-2x^3-2y^3+6xy+10

extreme f(x)=3x^2-2x+y^2-4y+1

extreme y=x^2-2ln(x)

Frequently Asked Questions (FAQ)

What is the extreme y= x/(x^2+9) ?
The extreme y= x/(x^2+9) is Minimum(-3,-1/6),Maximum(3, 1/6)