What is the extreme x/(x^2+10x+21) ?

The extreme x/(x^2+10x+21) is Minimum(-sqrt(21),(5+sqrt(21))/8),Maximum(sqrt(21),(5-sqrt(21))/8)

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extreme x/(x^2+10x+21)

extreme points

\frac{x}{x ^{2} + 10 x + 21}

Minimum (- 21, \frac{5 + 21}{8}), Maximum (21, \frac{5 - 21}{8})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 21}{( x ^{2} + 10 x + 21 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 7,

Decreasing

: - 7 < x < - 21,

Increasing

: - 21 < x < - 3,

Increasing

: - 3 < x < 21,

Decreasing

: 21 < x < \infty

Plug

x = - 21

into

\frac{x}{x ^{2} + 10 x + 21} : \frac{5 + 21}{8}

Minimum (- 21, \frac{5 + 21}{8})

Plug

x = 21

into

\frac{x}{x ^{2} + 10 x + 21} : \frac{5 - 21}{8}

Maximum (21, \frac{5 - 21}{8})

Minimum (- 21, \frac{5 + 21}{8}), Maximum (21, \frac{5 - 21}{8})

f (x) = x^{3} + 15 x^{2} - 33 x

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

f (x) = - \frac{1}{2} x^{4} + 2 x^{3} + 28 x^{2} + 18

f (x, y) = ln (x + y - 4)

f (x, y) = x^{2} + x y + y^{2} - 37 y + 456

What is the extreme x/(x^2+10x+21) ?
The extreme x/(x^2+10x+21) is Minimum(-sqrt(21),(5+sqrt(21))/8),Maximum(sqrt(21),(5-sqrt(21))/8)