Let C(x) be the cost of producing x units of a certain good. Assume that the graph

Question:

Let C(x) be the cost of producing x units of a certain good. Assume that the graph of C is concave up.
(a) Show that the average cost A(x) = C(x)/x is minimized at the production level x₀such that average cost equals marginal cost—that is, A(x₀) = C'(x₀).
(b) Show that the line through (0, 0) and (x₀,C(x₀)) is tangent to the graph of C.