Please help with this question; I'm desperate!?

Question

A bookbinder estimates that the cost C, in dollars, of making x school binders is modeled by the function C(x) = 2 + 2x + 0.017x^2. Determine the marginal cost of producing 100 binders.

Answer 1

The "marginal cost" means the incremental cost of the last book.

If this is for a calculus class, they probably want the derivative at the 100th book:

C(x) = 2 + 2x + 0.017x^2
C'(x) = 2 + 0.034x

C'(100) = 2 + 3.4 = $5.40

If it is not for calculus, they probably just want the cost of the 100th book, which is C(100) - C(99):

C(100) = 2 + 2(100) + 0.017(100^2)
C(100) = 202 + 170
C(100) = 372

C(99) = 2 + 2(99) + 0.017(99^2)
C(99) = 200 + 166.62
C(99) = 366.62

C(100) - C(99) = $5.38