What is the extreme f(x)=(10x)/(1+x^2) ?

The extreme f(x)=(10x)/(1+x^2) is Minimum(-1,-5),Maximum(1,5)

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extreme f(x)=(10x)/(1+x^2)

extreme points

f (x) = \frac{10 x}{1 + x ^{2}}

Minimum (- 1, - 5), Maximum (1, 5)

Solution steps

f^{'} (x) = \frac{10 ( 1 - x ^{2} )}{( 1 + x ^{2} ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

\frac{10 x}{1 + x ^{2}} : - 5

Minimum (- 1, - 5)

Plug

x = 1

into

\frac{10 x}{1 + x ^{2}} : 5

Maximum (1, 5)

Minimum (- 1, - 5), Maximum (1, 5)

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

f (x) = x^{3} - 3 x + 1, 0 \leq x \leq 5

f (x) = 3 x^{2} + 4 x - 4

f (x) = \frac{3 x}{2 x ^{2} + 2}, - 4 \leq x \leq 4

What is the extreme f(x)=(10x)/(1+x^2) ?
The extreme f(x)=(10x)/(1+x^2) is Minimum(-1,-5),Maximum(1,5)