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Popular >

extreme (5x)/(x^2+9)

Solution

extreme points

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

Solution

Minimum (- 3, - \frac{5}{6}), Maximum (3, \frac{5}{6})

Solution steps

f^{'} (x) = \frac{5 ( - 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{5 x}{x ^{2} + 9} : - \frac{5}{6}

Minimum (- 3, - \frac{5}{6})

Plug

x = 3

into

\frac{5 x}{x ^{2} + 9} : \frac{5}{6}

Maximum (3, \frac{5}{6})

Minimum (- 3, - \frac{5}{6}), Maximum (3, \frac{5}{6})

Popular Examples

extreme f(x)=(1+x/5)x^{2/3}extreme points

f (x) = (1 + \frac{x}{5}) x^{\frac{2}{3}}

extreme 3x+y extreme points

3 x + y

extreme f(x)=(e^x)/((3+e^x))extreme points

f (x) = \frac{e ^{x}}{( 3 + e ^{x} )}

extreme f(x)=-x^2+190 extreme points

f (x) = - x^{2} + 190

extreme f(x)=28x-(x^2)/(105)extreme points

f (x) = 28 x - \frac{x ^{2}}{105}

Frequently Asked Questions (FAQ)

What is the extreme (5x)/(x^2+9) ?
The extreme (5x)/(x^2+9) is Minimum(-3,-5/6),Maximum(3, 5/6)