Curvy calculus
In these resources from the CMEP website, you'll need to use your calculus cunning to solve problems involving various aspects of differentiation and integration.
Curvy Cubics Stage: 5 Challenge Level: 
Use some calculus clues to pin down an equation of a cubic graph.
Can You Find... Cubic Curves Stage: 5 Challenge Level:
Can you find equations for cubic curves that have specific features?
Integral Chasing Stage: 5 Challenge Level:
Can you find the missing constants from these not-quite-so-obvious definite integrals?
Designing a Polynomial Stage: 5 Challenge Level:
Can you find a polynomial function whose first derivative is equal to the function?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.