What is the extreme f(x)= x/(x^2+5x+4) ?

The extreme f(x)= x/(x^2+5x+4) is Minimum(-2,1),Maximum(2, 1/9)

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extreme f(x)= x/(x^2+5x+4)

extreme points

f (x) = \frac{x}{x ^{2} + 5 x + 4}

Minimum (- 2, 1), Maximum (2, \frac{1}{9})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 4}{( x ^{2} + 5 x + 4 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < - 2,

Increasing

: - 2 < x < - 1,

Increasing

: - 1 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

\frac{x}{x ^{2} + 5 x + 4} : 1

Minimum (- 2, 1)

Plug

x = 2

into

\frac{x}{x ^{2} + 5 x + 4} : \frac{1}{9}

Maximum (2, \frac{1}{9})

Minimum (- 2, 1), Maximum (2, \frac{1}{9})

2 ln (1 + x^{2})

(x - 1) e^{x + 1}

f (x) = sin (x) + cos (x), 0 < x < 2 π

f (x) = sin (x), - \frac{π}{2} \leq x \leq \frac{5 π}{6}

y = - x^{2} + 4 x

What is the extreme f(x)= x/(x^2+5x+4) ?
The extreme f(x)= x/(x^2+5x+4) is Minimum(-2,1),Maximum(2, 1/9)