AP Calculus ABmediummcq1 pt

A company is studying the cost of a new project. The total cost C(x) is given by the function C(x) = 1000 + 500x + 20x², where x is the number of units produced. Which of the following statements about the cost is true?

A.B) The cost is increasing at an increasing rate.
B.C) The cost is decreasing at a decreasing rate.
C.A) The cost is increasing at a decreasing rate.
D.D) The cost is decreasing at an increasing rate.

Explanation

Core Concept

This question tests the student's understanding of rates of change and the second derivative. The cost is increasing at an increasing rate, as the second derivative of C(x) is positive. Option A is incorrect because the cost is increasing, but at an increasing rate, not a decreasing rate. Option C is incorrect because the cost is increasing, not decreasing. Option D is incorrect because the cost is increasing, not decreasing.

Correct Answer

AB) The cost is increasing at an increasing rate.

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