Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.4 Exercises - Page 136: 35

Answer

When the tangent line of $f(x)$ is horizontal $f'(x) = 0$
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Work Step by Step

In this question you are asked to use technology to find the derivative of the expression $y = \frac{\sqrt x +1}{x^2 +1}$ and also to use the same technology to graph the function. The second part is explaining where the function corresponds to any zeros of the graph of the derivative. As you can see on the graph, when the tangent line is horizontal on $f(x)$ the graph of $f'(x)$ has a zero:
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