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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 5

into

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

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

Plug

x = 5

into

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

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

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

f (x, y) = x^{3} + y^{2} - 6 x y + 9 x + 5 y + 2

f (x, y) = 100 \cdot (y - x^{2})^{2} + (x - 1)^{2}

f (x) = x^{4} - 8 x^{3} + 9

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

y = x^{x}, x > 0

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