(a) Use a graphing calculator or computer to graph the circle x² + y² = 1. On the same screen, graph several curves of the form x² + y = c until you find two that just touch the circle. What is the significance of the values of c for these two curves?
(b) Use Lagrange multipliers to find the extreme values of f (x, y) = x² + y subject to the constraint x² + y² = 1. Compare your answers with those in part (a).