What is the extreme f(x)= x/(x^2-x+16) ?

The extreme f(x)= x/(x^2-x+16) is Minimum(-4,-1/9),Maximum(4, 1/7)

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extreme f(x)= x/(x^2-x+16)

extreme points

f (x) = \frac{x}{x ^{2} - x + 16}

Minimum (- 4, - \frac{1}{9}), Maximum (4, \frac{1}{7})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 16}{( x ^{2} - x + 16 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 4

into

\frac{x}{x ^{2} - x + 16} : - \frac{1}{9}

Minimum (- 4, - \frac{1}{9})

Plug

x = 4

into

\frac{x}{x ^{2} - x + 16} : \frac{1}{7}

Maximum (4, \frac{1}{7})

Minimum (- 4, - \frac{1}{9}), Maximum (4, \frac{1}{7})

f (x, y) = x^{3} + y^{3} - 6 x^{2} - \frac{3}{2} y^{2} + 9 x - 1

f (x) = \frac{x ^{3}}{3} - 5 x^{2} + 16 x - 100

f (x, y) = x y^{2} - 9 x^{2} - 2 y^{2}

f (x) = x^{2} + 4 x - 2

f (x, y) = 3 x + 5 y

What is the extreme f(x)= x/(x^2-x+16) ?
The extreme f(x)= x/(x^2-x+16) is Minimum(-4,-1/9),Maximum(4, 1/7)