What is the extreme (27x^2)/((2-x)^3) ?

The extreme (27x^2)/((2-x)^3) is Maximum(-4,2),Minimum(0,0)

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extreme (27x^2)/((2-x)^3)

extreme points

\frac{27 x ^{2}}{( 2 - x ) ^{3}}

Maximum (- 4, 2), Minimum (0, 0)

Solution steps

f^{'} (x) = \frac{27 x ( x + 4 )}{( 2 - x ) ^{4}}

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 0,

Increasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 4

into

\frac{27 x ^{2}}{( 2 - x ) ^{3}} : 2

Maximum (- 4, 2)

Plug

x = 0

into

\frac{27 x ^{2}}{( 2 - x ) ^{3}} : 0

Minimum (0, 0)

Maximum (- 4, 2), Minimum (0, 0)

\frac{8 x ^{2}}{x - 6}, - 3 \leq x \leq 2

f (x, y) = x + 3 y

g (x) = x^{3} - 12 x^{2} + 45 x + 4

g (x) = x^{3} - 12 x^{2} + 45 x + 1

g (x) = x^{3} - 12 x^{2} + 45 x + 2

What is the extreme (27x^2)/((2-x)^3) ?
The extreme (27x^2)/((2-x)^3) is Maximum(-4,2),Minimum(0,0)