Let . The average value of the function over the interval is

The trapezium method approximation for the area between the graph of  and the horizontal axis over the interval  is:

Given that, then is equal to

A flat rectangular cardboard sheet with width and length has a square of length cut out from each corner, where . The edges are then folded up to form a rectangular box with an open top. The volume of the box has:

Given the function . Find all its stationary points and state their nature.

The graph of the function is shown below.

The graph of the gradient function could be given by:

Let .

The gradient of the graph of is negative for

Given that , the value of is 

If , then is equal to