What is the extreme f(x)=(27x^2)/((1-x)^3) ?

The extreme f(x)=(27x^2)/((1-x)^3) is Maximum(-2,4),Minimum(0,0)

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extreme f(x)=(27x^2)/((1-x)^3)

extreme points

f (x) = \frac{27 x ^{2}}{( 1 - x ) ^{3}}

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

Solution steps

f^{'} (x) = \frac{27 x ( x + 2 )}{( 1 - x ) ^{4}}

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

\frac{27 x ^{2}}{( 1 - x ) ^{3}} : 4

Maximum (- 2, 4)

Plug

x = 0

into

\frac{27 x ^{2}}{( 1 - x ) ^{3}} : 0

Minimum (0, 0)

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

f (x) = 345 x^{2} - 3450 x^{3}, 0 \leq x \leq 0.1

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} + 1

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

f (x, y) = x^{3} + y^{2} - 4 x y + 17 x - 10 y + 2021

f (x) = (x - 3) (x - 2)^{2}

What is the extreme f(x)=(27x^2)/((1-x)^3) ?
The extreme f(x)=(27x^2)/((1-x)^3) is Maximum(-2,4),Minimum(0,0)