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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
If you go along the edge a distance $x$ then head straight for the far corner can you work out the time taken as a function of $x$?