Calculus generally

problem
Operating machines

Age

16 to 18

Challenge level

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
problem
Implicitly

Age

16 to 18

Challenge level

Can you find the maximum value of the curve defined by this expression?
problem
Power up

Age

16 to 18

Challenge level

Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x
problem
2D-3D

Age

16 to 18

Challenge level

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?
article
Fractional calculus III

Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.
article
Fractional calculus II

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.
article
Fractional calculus I

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.