Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 4: Applications of Derivatives - Section 4.4 - Concavity and Curve Sketching - Exercises 4.4 - Page 214: 99

Answer

At about $x=60,000$ units produced.

Work Step by Step

Marginal cost is defined as $f'(x)=\displaystyle \frac{dc}{dx}.$ $f'(x)$ increases where $f''(x) \gt 0 $ and decreases where $f''(x) \lt 0$ . The left part of the graph is concave down, $f''(x) \lt 0$, and at approximately $x=60$ there is an inflection point, where concavity changes to up, $f''(x) \gt 0.$ Thus, marginal cost $f'(x)$ changes from decreasing to increasing at about $x=60,000$ units produced.
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