This problem challenges you to sketch curves with different properties.
You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.
Here explore some ideas of how the definitions and methods of calculus change if you integrate or differentiate n times when n is not a whole number.
Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.
Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other. What is the volume of intersection?
Can you hit the target functions using a set of input functions and a little calculus and algebra?
Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.
Consider these analogies for helping to understand key concepts in calculus.
Mathmo is a revision tool for post-16 mathematics. Give yourself a mathematical workout!
Find the relationship between the locations of points of inflection, maxima and minima of functions.
