The following are AC and TC functions for various firms
(i). AC = 140/Q + 20
(ii) AC - a/Q = k
(iii) TC - 10 =2Q + 0.1Q^{2}
(iv) TC - k - βQ = cQ^{2}
Where a, k, β and c are positive constants.
(a) Find the expression for the gradients of the AC functions
(b) For what values of Q will AC be decreasing?
(c) Which functions will give U-shaped AC curves?