Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.2 The Derivative as a Function - Exercises - Page 115: 50


$ x=2$, $ x=-2$

Work Step by Step

The tangent line is horizontal when the slope is 0. This implies that $ f'(x)=0$. $ f'(x)=\frac{d}{dx}(12x-x^{3})=12\times\frac{d}{dx}(x)-\frac{d}{dx}(x^{3})$ $=(12\times1)-3x^{3-1}=12-3x^{2}$ $12-3x^{2}=0$ when $ x=2$ or $ x=-2$
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