What is the extreme (x^3)/(x^2+4) ?

The extreme (x^3)/(x^2+4) is Saddle(0,0)

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extreme (x^3)/(x^2+4)

extreme points

\frac{x ^{3}}{x ^{2} + 4}

Saddle (0, 0)

Solution steps

Find the critical points:

x = 0

Domain of

\frac{x ^{3}}{x ^{2} + 4} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \infty

Plug the extreme point

x = 0

into

\frac{x ^{3}}{x ^{2} + 4} \Rightarrow y = 0

Saddle (0, 0)

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

x^{3} + 3 x^{2} y + y^{3} - y

f (x, y) = - 8 x y - 5 x^{2} - 6 y^{2} + 38 x + 36 y + 7

f (x, y) = x^{2} + 2 y^{2} - 8 x + 8 y

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