The curve given implicitly by x^ 2 y + y^ 3 =8 contains a branch with for

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The curve given implicitly by

x^{2}y + y^{3}=8

contains a branch with

y>0

for

-1<x<1

. For this branch, determine on which of the intervals

(-1,0)

and

(0,1)

the function y(x) is increasing and on which it is decreasing.