What is the extreme f(x)= x/((x^2+4)) ?

The extreme f(x)= x/((x^2+4)) is Minimum(-2,-1/4),Maximum(2, 1/4)

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extreme f(x)= x/((x^2+4))

extreme points

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

Minimum (- 2, - \frac{1}{4}), Maximum (2, \frac{1}{4})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

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

Minimum (- 2, - \frac{1}{4})

Plug

x = 2

into

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

Maximum (2, \frac{1}{4})

Minimum (- 2, - \frac{1}{4}), Maximum (2, \frac{1}{4})

f (x) = - 0.5 x^{2}

f (x) = 5 x e^{- 5 x}

y = x^{3} - 3 x^{2} - 9 x

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

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

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