You may also like

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:
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 $b$.