Differentiation

Draw graphs of the sine and modulus functions and explain the humps.

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.