Posted by **ravinder** on Thursday, November 22, 2012 at 9:45pm.

Find the first and second derivative of the function

y=f(x)=x^3/(1-(x^2))

Use the information about the derivatives to determine any local maxima and minima, regions where the curve iss concave up or down, and any inflection points

- math -
**Steve**, Thursday, November 22, 2012 at 11:54pm
y = x^3/(1-x^2)

y' = -x^2(x-3)/(1-x^2)^2

y'' = -2x(x^2+3)/(1-x^2)^3

since the denominator is always positive or 0, y' and y'' are zero when the numerators are zero, and undefined at x=±1.

Now it should be easy to read off the increasing/decreasing/concavity intervals.

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