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

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

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

extreme points

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

Minimum (- 4, - \frac{2}{27}), Maximum (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 0,

Decreasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 4

into

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

Minimum (- 4, - \frac{2}{27})

Plug

x = 0

into

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

Maximum (0, 0)

Minimum (- 4, - \frac{2}{27}), Maximum (0, 0)

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