What is the extreme (x+3)/(x^3+2x^2-15x-36) ?

The extreme (x+3)/(x^3+2x^2-15x-36) is Maximum(1/2 ,-4/49)

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extreme (x+3)/(x^3+2x^2-15x-36)

extreme points

\frac{x + 3}{x ^{3} + 2 x ^{2} - 15 x - 36}

Maximum (\frac{1}{2}, - \frac{4}{49})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Increasing

: - 3 < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = \frac{1}{2}

into

\frac{x + 3}{x ^{3} + 2 x ^{2} - 15 x - 36} : - \frac{4}{49}

Maximum (\frac{1}{2}, - \frac{4}{49})

f (x) = \frac{4 x}{x ^{2} + 3}

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

\frac{5 x - 3}{36 - x ^{2}}

f (x) = f (x) = x + \frac{25}{x} + 9, 1 \leq x \leq 50

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

What is the extreme (x+3)/(x^3+2x^2-15x-36) ?
The extreme (x+3)/(x^3+2x^2-15x-36) is Maximum(1/2 ,-4/49)