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

The extreme f(x)= x/(25-x+x^2) is Minimum(-5,-1/11),Maximum(5, 1/9)

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

extreme points

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

Minimum (- 5, - \frac{1}{11}), Maximum (5, \frac{1}{9})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 5

into

\frac{x}{25 - x + x ^{2}} : - \frac{1}{11}

Minimum (- 5, - \frac{1}{11})

Plug

x = 5

into

\frac{x}{25 - x + x ^{2}} : \frac{1}{9}

Maximum (5, \frac{1}{9})

Minimum (- 5, - \frac{1}{11}), Maximum (5, \frac{1}{9})

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

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

(x^{2} + 12) (144 - x^{2})

f (x) = \frac{10 x ^{3}}{3} - \frac{11 x ^{2}}{2} + x + 2

5 + 4 x^{2} - x^{4}

What is the extreme f(x)= x/(25-x+x^2) ?
The extreme f(x)= x/(25-x+x^2) is Minimum(-5,-1/11),Maximum(5, 1/9)