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

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

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

extreme points

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

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

Solution steps

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

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

Plug

x = 5

into

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

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

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

f (x) = \frac{x + 3}{3 x - 27} + \frac{1}{x ^{2} - 4}

\frac{10 - x}{x ^{2} - 1}

f (x) = - 2 x - 10

y = - 3 + 5

sin (3 x)

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