Final Exam Study Guide Problem 6 Solution

In this problem you need to take a derivative in the form of marginal cost and undo the derivative to get the cost function. This is covered in Question 4 of Section13.1.

Problem 6 The marginal cost function for a product is final_exam_sg_6a. If 10 units costs $94.20, find the cost function C(x).

Solution To find the cost function C(x), we need to take the antiderivative of ’(x):

final_exam_sg_6b

To find K, we need to substitute 10 for x and set the result equal to 94.20:

final_exam_sg_6c

Solve for K to get

final_exam_sg_6d

This makes the cost function approximately

final_exam_sg_6e