Problem 3 Consider the following production function: y = f(x1, x2) = 0.4x12 + 0.6x,2 -1/2 (a) Use the implicit-function theorem to find the marginal rate of technical substitution dx2/dx1 corresponding to this production function. (b) Show that the isoquants corresponding to this production function are convex. [Hint: Differentiate the formula you have computed for dx2 /dx, to find an expres- sion for the second-order derivative d2x2/ dx3. ]