Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 13 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Section 13.4 The Tangent Problem; The Derivative - 13.4 Assess Your Understanding - Page 916: 6

Answer

True

Work Step by Step

Let us say that the secant line is connected to the points $(x,f(x))$ and $(c, f(c))$ . If the point $(c, f(c))$ is kept fixed, while $x \to c$, then the two points get closer to each other and the secant line becomes the tangent line. Put another way, the secant line connects two points on a graph, while the tangent line gives the slope of one point. When the two points get closer together, the two points become one and the tangent line and secant line match. So, the given statement is True.
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