Given a function, determine rising and falling intervals, concavity, critical points, points of inflection.
y = x(x-4)^3
In a function like this, would you expand everything and then try to do it or use the product rule? If you use product rule, the derivatives are a bit complex and I find it hard to see how to isolate x to determine when the functions are zero (to find certain points). Can someone show by example how to approach this?