Suppose the total cost in dollars of manufacturing q units is given by the function C(q) = 3q^2+4q+48.
a) Express the average manufacturing cost per unit as a function of q.
b) For what value of q is the average cost the smallest?
c) For what value of q is the average cost equal to the marginal cost?
d) Graph the total cost, marginal cost, and average cost on the same set of axes.
Average Cost = C(q)/q
=(3q^2 + 4q +48)/q
=3q + 4 + (48/q)
Marginal Average Cost = AC'(x)
=3 + 48/q^2
0=3+(48/q^2)
-3 = 48/q^2
-3q^2 = 48
q^2 = -16
q = (+/-)4
Average cost = Marginal Cost
3q^2+4q+48 = (+/-)4
I know I haven't finished solving - I'm not sure if I have set this problem correctly.