What is the extreme x/(x^2+13x+36) ?

The extreme x/(x^2+13x+36) is Minimum(-6,1),Maximum(6, 1/25)

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extreme x/(x^2+13x+36)

extreme points

\frac{x}{x ^{2} + 13 x + 36}

Minimum (- 6, 1), Maximum (6, \frac{1}{25})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 36}{( x ^{2} + 13 x + 36 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 9,

Decreasing

: - 9 < x < - 6,

Increasing

: - 6 < x < - 4,

Increasing

: - 4 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = - 6

into

\frac{x}{x ^{2} + 13 x + 36} : 1

Minimum (- 6, 1)

Plug

x = 6

into

\frac{x}{x ^{2} + 13 x + 36} : \frac{1}{25}

Maximum (6, \frac{1}{25})

Minimum (- 6, 1), Maximum (6, \frac{1}{25})

f (x) = 2 x^{3} - 12 x^{2} + 6

f (x) = 2 x^{3} - 12 x^{2} + 4

f (x) = x^{3} - 6 x^{2} + 12 x + 4

f (x) = x^{\frac{2}{3}} - 1

f (x) = 48 x y - 32 x^{3} - 24 y^{2}

What is the extreme x/(x^2+13x+36) ?
The extreme x/(x^2+13x+36) is Minimum(-6,1),Maximum(6, 1/25)