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Generally Geometric

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

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

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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.

Quick Route

Stage: 5 Challenge Level: Challenge Level:1
Students: Some students will have learnt the chain rule for differentiation but if you have not learnt the chain rule then how about finding out how it works in order to solve this, and many more, problems?

Teachers: One teaching style introduces the processes and later comes to applications. Another style uses an application to introduce and motivate the need to learn a process.