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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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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.

Calculus Countdown

Age 16 to 18 Challenge Level:
To begin with, try acting on the starting functions with various operators to see the sorts of possibilities that occur.

To hit a target, think what functions would be needed to make them in one step. How might I arrive at these inputs?