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Popular >

extreme (3x)/(x^2+1)

Solution

extreme points

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

Solution

Minimum (- 1, - \frac{3}{2}), Maximum (1, \frac{3}{2})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, - \frac{3}{2})

Plug

x = 1

into

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

Maximum (1, \frac{3}{2})

Minimum (- 1, - \frac{3}{2}), Maximum (1, \frac{3}{2})

Graph

Popular Examples

extreme f(x)=-34x^2+550x extreme points

f (x) = - 34 x^{2} + 550 x

extreme f(x)=sqrt(x)ln(9x),(0,infinity)extreme points

f (x) = x ln (9 x), (0, \infty)

extreme x^4-2x^3+x+1 extreme points

x^{4} - 2 x^{3} + x + 1

extreme-(8*x)/(x^2+1)extreme points

- \frac{8 \cdot x}{x ^{2} + 1}

extreme (x^2)/(x^2-36)extreme points

\frac{x ^{2}}{x ^{2} - 36}

Frequently Asked Questions (FAQ)

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