Consider the function f(x, y) = 5x 2 + 2y 3 . Find the maximum and minimum value of f subject to the constraint x 2 + y 2 = 1; then find the maximum and minimum values of f subject to the constraint x 2 + y 2 = 4. Note that the constraints only differ by the constant they are equal to. This problem is inviting you to consider what aspects of the optimisation problem are identical in the two cases, and what aspects will be changed. Creating a tool along the lines of the one used in Q4 of the tutorial might help your intuition.