Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - Chapter 2 Review Exercises - Page 185: 27

Answer

Same slope

Work Step by Step

The slope of the secant line is $\frac{b^2-a^2}{b-a} = a+b$ The instantaneous slope at $x=\frac{1}{2}(a+b)$ is $f'(x) = 2x = 2 (\frac{1}{2}(a+b)) = a+b$ Thus, both slopes are equal. The graph below illustrates this as the secant line, in green, is parallel and has the same slope as the tangent line, in purple.
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