What is the extreme f(x)=-(50x)/(x^2+25) ?

The extreme f(x)=-(50x)/(x^2+25) is Maximum(-5,5),Minimum(5,-5)

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extreme f(x)=-(50x)/(x^2+25)

extreme

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

Solution steps

f^{'} (x) = - \frac{50 ( - 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{50 x}{x ^{2} + 25} : 5

Maximum (- 5, 5)

Plug

x = 5

into

- \frac{50 x}{x ^{2} + 25} : - 5

Minimum (5, - 5)

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

What is the extreme f(x)=-(50x)/(x^2+25) ?
The extreme f(x)=-(50x)/(x^2+25) is Maximum(-5,5),Minimum(5,-5)