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

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

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

extreme points

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

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

Solution steps

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

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

Plug

x = 1

into

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

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

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

y = 13 x^{4} + 4 x^{2} + 3

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

f (x) = \frac{2 x ^{2}}{x - 4}

f (x) = x^{3} + 2 x^{2} - 7 x, 0 \leq x \leq 2

f (x) = 2 x^{3} - 21 x^{2} + 72 x - 72.5

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