Chapter 5.5, Problem 1MP

Matched Problem 1 Repeat Example 1 for the daily cost function

C(x) = −7.5x² + 305x + 625

EXAMPLE 1 Change in Cost vs Area under Marginal Cost The daily cost function for a company (in dollars) is given by

$\begin{array}{cc}C\left(x\right)=-7.5x^2+305x+625& 0\le x\le 20\end{array}$

(A)    Graph C(x) for 0 ≤ x ≤ 20, calculate the change in cost from x = 5 to x = 10, and indicate that change in cost on the graph.

(B)    Graph the marginal cost function C′(x) for 0 ≤ x ≤ 20, and use geometric formulas (see Appendix C) to calculate the area between C′(x) and the x axis from x = 5 to x = 10.

1. (C)  Compare the results of the calculations in parts (A) and (B).