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Popular >

extreme (4x)/(x^2+1)

Solution

extreme points

\frac{4 x}{x ^{2} + 1}

Solution

Minimum (- 1, - 2), Maximum (1, 2)

Solution steps

f^{'} (x) = \frac{4 ( - 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{4 x}{x ^{2} + 1} : - 2

Minimum (- 1, - 2)

Plug

x = 1

into

\frac{4 x}{x ^{2} + 1} : 2

Maximum (1, 2)

Minimum (- 1, - 2), Maximum (1, 2)

Graph

Popular Examples

extreme-2/(x^2-4)extreme points

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

extreme f(x,y)=xy+4/x+2/y extreme points

f (x, y) = x y + \frac{4}{x} + \frac{2}{y}

extreme f(x)= 2/(x^2+3)extreme points

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

extreme f(x)=x^2(x^2-1)extreme points

f (x) = x^{2} (x^{2} - 1)

extreme f(x)= x/(x^2-1),(0,5)extreme points

f (x) = \frac{x}{x ^{2} - 1}, (0, 5)

Frequently Asked Questions (FAQ)

What is the extreme (4x)/(x^2+1) ?
The extreme (4x)/(x^2+1) is Minimum(-1,-2),Maximum(1,2)