Calculus meets Functions

Many ways problem

Problem

It would be a good idea to try to sketch some of the cubics first before trying to form an equation.

Can you find a cubic curve that…

1. … has no stationary points?

2. … has two stationary points: one when $x=2$ and another when $x=5$?

3. … has a local minimum when $x=-1$?

4. … has a local minimum when $x=-2$ and a local maximum when $x=4$?