Suppose you want to make a container from aluminium sheet. The container is cylindrical in shape, with radius r and height h, has no lid, and needs to hold 235mL of water.

a) express the surface area A of the container in terms of r only.

b) find the critical point of A and determine the surface area of the container at the critical point.

c) use the second derivative test to show that the surface area of the container has a global minimum at the critical point.