This resource is from Underground Mathematics.
Can you find a cubic curve that...
(a) ... has no stationary points?
(b) ... has two stationary points: one when $x=2$ and one when $x=5$?
(c) ... has a local minimum when $x=-1$?
(d) ... has a local minimum when $x=-2$ and a local maximum when $x=4$?
It would be a good idea to try and sketch
some of the cubics first before trying to form an equation.
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