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.

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

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

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

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

Put your complex numbers and calculus to the test with this impedance calculation.

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.