What is the extreme f(x)=((x-2)^2)/(x+6) ?

The extreme f(x)=((x-2)^2)/(x+6) is Maximum(-14,-32),Minimum(2,0)

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extreme f(x)=((x-2)^2)/(x+6)

extreme points

f (x) = \frac{( x - 2 ) ^{2}}{x + 6}

Maximum (- 14, - 32), Minimum (2, 0)

Solution steps

f^{'} (x) = \frac{x ^{2} + 12 x - 28}{( x + 6 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 14,

Decreasing

: - 14 < x < - 6,

Decreasing

: - 6 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 14

into

\frac{( x - 2 ) ^{2}}{x + 6} : - 32

Maximum (- 14, - 32)

Plug

x = 2

into

\frac{( x - 2 ) ^{2}}{x + 6} : 0

Minimum (2, 0)

Maximum (- 14, - 32), Minimum (2, 0)

f (x) = cot (x) + tan (x)

f (x) = x^{3} + y^{3} + 4 x y

f (x) = 6 x - 24

f (x) = 6 x - 30

f (x) = 9 z + 61 x + 2 x - 4

What is the extreme f(x)=((x-2)^2)/(x+6) ?
The extreme f(x)=((x-2)^2)/(x+6) is Maximum(-14,-32),Minimum(2,0)