What is the extreme y=(x^3)/(x^2-4) ?

The extreme y=(x^3)/(x^2-4) is Maximum(-2sqrt(3),-3sqrt(3)),Saddle(0,0),Minimum(2sqrt(3),3sqrt(3))

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extreme y=(x^3)/(x^2-4)

extreme points

y = \frac{x ^{3}}{x ^{2} - 4}

Maximum (- 23, - 33), Saddle (0, 0), Minimum (23, 33)

Solution steps

f^{'} (x) = \frac{x ^{4} - 12 x ^{2}}{( x ^{2} - 4 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 23,

Decreasing

: - 23 < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Decreasing

: 2 < x < 23,

Increasing

: 23 < x < \infty

Plug

x = - 23

into

\frac{x ^{3}}{x ^{2} - 4} : - 33

Maximum (- 23, - 33)

Plug

x = 0

into

\frac{x ^{3}}{x ^{2} - 4} : 0

Saddle (0, 0)

Plug

x = 23

into

\frac{x ^{3}}{x ^{2} - 4} : 33

Minimum (23, 33)

Maximum (- 23, - 33), Saddle (0, 0), Minimum (23, 33)

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