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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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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.

Bend

Stage: 5 Challenge Level: Challenge Level:1
Some elementary calculus and trigonometry are required here and some perseverance. You should expect the final answer to be an expression symmetric in $a$ and $b$.