problem Favourite Exponential Trend Age 16 to 18 Challenge level 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.
problem Favourite Quick Route Age 16 to 18 Challenge level What is the quickest route across a ploughed field when your speed around the edge is greater?
problem What's my equation? Age 16 to 18 Challenge level Can you find the differential equations giving rise to these famous solutions?