What is the extreme f(x)=-(10x)/(x^2+25) ?

The extreme f(x)=-(10x)/(x^2+25) is Maximum(-5,1),Minimum(5,-1)

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extreme f(x)=-(10x)/(x^2+25)

extreme points

f (x) = - \frac{10 x}{x ^{2} + 25}

Maximum (- 5, 1), Minimum (5, - 1)

Solution steps

f^{'} (x) = - \frac{10 ( - x ^{2} + 25 )}{( x ^{2} + 25 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 5

into

- \frac{10 x}{x ^{2} + 25} : 1

Maximum (- 5, 1)

Plug

x = 5

into

- \frac{10 x}{x ^{2} + 25} : - 1

Minimum (5, - 1)

Maximum (- 5, 1), Minimum (5, - 1)

y = cos (2 x)

1.5 cos (6 x - 3.2)

\frac{3 x}{x + 9}

f (x) = 3

\frac{x ^{2} + 8 x + 15}{x + 5}

What is the extreme f(x)=-(10x)/(x^2+25) ?
The extreme f(x)=-(10x)/(x^2+25) is Maximum(-5,1),Minimum(5,-1)