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

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

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

extreme points

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

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

Solution steps

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

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

Plug

x = 1

into

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

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

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

f (x, y) = 2 x^{3} + 2 y^{3} - 9 x^{2} + 3 y^{2} - 12 y

f (x) = x^{5} - 15 x^{3}

f (x, y) = x y - \frac{1}{x} - \frac{1}{y}

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

f (x) = e^{x} (15 - x^{2})

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