11. Find dy/dar by implicit differentiation [(a), (b), and (c)] (a) Vry = 1+ry, (b) xcosy + y cost = 1, (c) =y. Hint for (c): Use logarithmic differentiation: ylnr = alny, then differentiate both sides with respect to r. (d) Given arcos(f(x)) + f(x) cose = 1. Find f(0) and f'(0). Write the equation of the tangent line to the graph of y = f(x) at the point (0, f(0)). 12. The cost (in dollars) of producing units of a certain commodity is C (x) = 5000 + 10r + 0.05x2. (a) Find the average rate of change of C(x) with respect to a when the production level is changed from r = 100 to r = 105. (b) Find the instantaneous rate of change of C(r) with respect to r when r = 100. (This is called the marginal cost.)