Problem
A note card company has found that the marginal cost per card of producing $x$ note cards is given by the function below, where $C^{\prime}(x)$ is the marginal cost, in cents, per card. Find the total cost of producing 760 cards, disregarding any fixed costs. \[ C^{\prime}(x)=-0.06 x+86, \text { for } x \leq 1000 \] The total cost is cents
Solution
Step 1 ：The total cost of producing $x$ cards is the integral of the marginal cost function from 0 to $x$. In this case, we need to integrate the function $C'(x) = -0.06x + 86$ from 0 to 760 to find the total cost of producing 760 cards.
Step 2 ：The total cost of producing 760 cards is \(\boxed{48032}\) cents.
