Differentiation

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.

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.

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

What is the quickest route across a ploughed field when your speed around the edge is greater?

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.

Can you match the charts of these functions to the charts of their integrals?

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

Can you hit the target functions using a set of input functions and a little calculus and algebra?

Look at the calculus behind the simple act of a car going over a step.