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


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

Exponential Trend

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.

Integration Matcher

Age 16 to 18
Challenge Level
The graphs of six functions and the graphs of their integrals have been mixed up below. Can you match them together?

Chart A
Chart B
Chart C
Chart D
Chart E
Chart F
Chart G
Chart H
Chart I
Chart J
Chart K
Chart L

You might like to print off copies of the graphs: Integration Matcher

What strategies did you use to match them up?

Can you make suggestions of algebraic forms for the functions used? You could plot your functions in GeoGebra or Desmos to see if your suggestions match the graphs.