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

The extreme f(x)=(3x^2)/(x-2) is Maximum(0,0),Minimum(4,24)

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

extreme points

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

Maximum (0, 0), Minimum (4, 24)

Solution steps

f^{'} (x) = \frac{3 ( x ^{2} - 4 x )}{( x - 2 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Decreasing

: 2 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = 4

into

\frac{3 x ^{2}}{x - 2} : 24

Minimum (4, 24)

Maximum (0, 0), Minimum (4, 24)

\frac{5 - x}{x + 2}

f (x) = x^{2} - 9 x + 14

f (x) = e^{2 x} - 4 e^{x}

f (x) = 4 x^{3} + 21 x^{2} + 36 x - 20

\frac{x ^{2} - 15}{x - 4}

What is the extreme f(x)=(3x^2)/(x-2) ?
The extreme f(x)=(3x^2)/(x-2) is Maximum(0,0),Minimum(4,24)