What is the extreme f(x)=(5x)/(x^2+25) ?

The extreme f(x)=(5x)/(x^2+25) is Minimum(-5,-1/2),Maximum(5, 1/2)

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extreme f(x)=(5x)/(x^2+25)

extreme points

f (x) = \frac{5 x}{x ^{2} + 25}

Minimum (- 5, - \frac{1}{2}), Maximum (5, \frac{1}{2})

Solution steps

f^{'} (x) = \frac{5 ( - x ^{2} + 25 )}{( x ^{2} + 25 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 5

into

\frac{5 x}{x ^{2} + 25} : - \frac{1}{2}

Minimum (- 5, - \frac{1}{2})

Plug

x = 5

into

\frac{5 x}{x ^{2} + 25} : \frac{1}{2}

Maximum (5, \frac{1}{2})

Minimum (- 5, - \frac{1}{2}), Maximum (5, \frac{1}{2})

f (x) = - x^{3} + 12 x - 18

y = (x - 1)^{5}

f (x) = - x^{3} + 12 x - 25

f (x) = - x^{3} + 12 x - 23

f (x) = \frac{1}{3} x^{3} + 3 x^{2} + 5 x - \frac{11}{3}

What is the extreme f(x)=(5x)/(x^2+25) ?
The extreme f(x)=(5x)/(x^2+25) is Minimum(-5,-1/2),Maximum(5, 1/2)