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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.

Integration Matcher

Age 16 to 18 Challenge Level:

Differentiation relates to gradients and integration relates to areas.

The two are inverse procedures.