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

The extreme f(x)=(x^3)/(3-x^2) is Minimum(-3, 9/2),Saddle(0,0),Maximum(3,-9/2)

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

extreme points

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

Minimum (- 3, \frac{9}{2}), Saddle (0, 0), Maximum (3, - \frac{9}{2})

Solution steps

f^{'} (x) = \frac{9 x ^{2} - x ^{4}}{( 3 - x ^{2} ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < 3,

Increasing

: 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

\frac{x ^{3}}{3 - x ^{2}} : \frac{9}{2}

Minimum (- 3, \frac{9}{2})

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 3

into

\frac{x ^{3}}{3 - x ^{2}} : - \frac{9}{2}

Maximum (3, - \frac{9}{2})

Minimum (- 3, \frac{9}{2}), Saddle (0, 0), Maximum (3, - \frac{9}{2})

f (x) = - \frac{6 x}{3 x ^{2} + 8}

f (x, y) = 2 x^{3} + y^{3} + 3 x^{2} - 3 y - 12 x - 4

Y (A, B) = A B + A B + A B

x^{2} - x

f (x) = x^{\frac{4}{3}} (7 x^{2} + 10 x - 210)

What is the extreme f(x)=(x^3)/(3-x^2) ?
The extreme f(x)=(x^3)/(3-x^2) is Minimum(-3, 9/2),Saddle(0,0),Maximum(3,-9/2)