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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.

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.


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.


Age 16 to 18 Challenge Level:
Work out the length of the straight line at an angle $\theta$ say to one wall which just touches the inner corner in terms of $a,\ b$ and $\theta$. This length will change as $\theta$ changes and it won't be possible to manoeuvre an object around the corner which is longer then the minimum value of this length.