This resource is from Underground Mathematics (previously known as the Cambridge Mathematics Education Project).
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.
This is an Underground Mathematics resource.
Underground Mathematics is funded by a grant from the UK Department for Education and provides free web-based resources that support the teaching and learning of post-16 mathematics. It started in 2012 as the Cambridge Mathematics Education Project (CMEP).
Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.