Suppose the cost of producing x widgets is $C(x)= 5000+40x-0.02x^2$.
A. What is the cost of producing widget number 31? Your answer should be a single number.
(Recall that $C(x)$ is the cost of producing numbers $1,2,3,\dots$ up to $x$).
B. What is the marginal cost when x=30?
For 1A I just plugged in $31$ to the $x$'s in the equation. My answer turned out to be $6259.224$. That isn't right because it said it should be a single number.
Since I don't believe my answer for 1A is right I'm not sure how to go about getting 1B.
The cost of producing widget number $31$ is the cost of producing $31$ widgets minus the cost of producing $30$ widgets which is:
$C(31) - C(30) $
$=(5000 + 40 \cdot 31 - 0.02 \cdot 31^2) - (5000 + 40 \cdot 30 - 0.02 \cdot 30^2)$
$= \$38.78$
Marginal cost is defined as $C'(x)$.
$C'(x) = 40 - 0.04x$
$C'(30) = 40 - 0.04 \cdot 30 = 40 - 1.20 = \$38.80$