Suppose the cost in dollars to produce x hundreds of nails is given by

C(x) = x² + 4x + 7.
(a) Sketch a graph of C(x).
(b) Find a formula for C(x + 1) - C(x), the cost to produce an additional hundred nails when x hundred are already produced. (This quantity is approximately equal to the marginal cost.)
(c) Find a formula for A(x), the average cost per hundred nails.
(d) Find a formula for A(x + 1) - A(x), the change in the average cost per nail when one additional batch of 100 nails is produced. (This quantity is approximately equal to the marginal average cost, which will be discussed in the chapter on the derivative.)