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Bend

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.

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Slide

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.

Generally Geometric

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2
Differentiating the known sum, then differentiating the series term by term and multiplying by $x$ gives the first result. I f this method works once it will work twice or $k$ times.