1. Find and classify the critical points of the following functions. (a) f(x, y) = - y (b) g(x, y) = rsin(y) (c) h(x, y) = (1+ 2) (1+2) ( 2+;) 2. The material used to make the bottom of a rectangular box is twice as expensive per unit area as the material used to make the top or side walls. Suppose that the box must have a fixed volume V. Find the dimensions (as an expression in terms of V) of the box for which the cost of materials is minimized. Justify your answer (why it provides a global minimum). 3. Consider the function f(r, y) described by the contour diagram, where level curves f(x, y) = k are plotted for different values of k. Let R = {(x, y) | 0.4