### 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.

### 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:
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.