Question

PLEASE HELP
Let C(q) represent the total cost of producing q items. Then C′(q) gives the marginal cost in dollars per item. Suppose a company determines that C(13)=2800 and C′(13)=73. Estimate the total cost of producing the following number of items. Your answers should be whole numbers.

a) 12 items

Answer 1

You could use the tangent line approximation: \[
\frac{L(q)-C(q_0)}{q-q_0}=C'(q_0) \implies L(q)=(q-q_0)C'(q_0)+C(q_0)
\]Basically, \(L(q)\) is a linear approximation of \(C(q)\)
\(q_0\) is the point for which we have the derivative (in this case \(13\))
\(q\) is the point we are trying to approximate at (in this case \(12\))

Answer 2

ok

Answer 3

so how do we plug into that

Answer 4

Use the right most equality I gave you, and plug in the values for \(q\) and \(q_0\) which I specified.

Answer 5

ok

Answer 6

and

Answer 7

@wio what'd u get