Can You Find... Cubic Curves
Age 16 to 18
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.
This is an Underground Mathematics resource.
Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.
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.