Question

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

Answer 1

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.