What is the extreme f(x)=(x+2)/((x+1)(2-x)) ?

The extreme f(x)=(x+2)/((x+1)(2-x)) is Maximum(-4, 1/9),Minimum(0,1)

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extreme f(x)=(x+2)/((x+1)(2-x))

extreme points

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

Maximum (- 4, \frac{1}{9}), Minimum (0, 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 4

into

\frac{x + 2}{( x + 1 ) ( 2 - x )} : \frac{1}{9}

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

Plug

x = 0

into

\frac{x + 2}{( x + 1 ) ( 2 - x )} : 1

Minimum (0, 1)

Maximum (- 4, \frac{1}{9}), Minimum (0, 1)

4 + \frac{9 x - 36}{( x - 4 ) ^{2} + 65}

f (x) = \frac{- 125}{4} x^{4} + x

f (x) = ln (x^{2} - 6 x - 7)

f (x) = sin (2 π x)

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

What is the extreme f(x)=(x+2)/((x+1)(2-x)) ?
The extreme f(x)=(x+2)/((x+1)(2-x)) is Maximum(-4, 1/9),Minimum(0,1)