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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 link

Curvy Cubics live

Stage: 5 Challenge Level: Challenge Level:1

Use some calculus clues to pin down an equation of a cubic graph.

Can You Find... Cubic Curves link

Can You Find... Cubic Curves live

Stage: 5 Challenge Level: Challenge Level:1

Can you find equations for cubic curves that have specific features?

Integral Chasing link

Integral Chasing live

Stage: 5 Challenge Level: Challenge Level:1

Can you find the missing constants from these not-quite-so-obvious definite integrals?

Designing a Polynomial link

Designing a Polynomial 

Stage: 5 Challenge Level: Challenge Level:1

Can you find a polynomial function whose first derivative is equal to the function?