Calculus, 10th Edition (Anton)

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

Chapter 3 - The Derivative In Graphing And Applications - 3.2 Analysis Of Functions II: Relative Extrema; Graphing Polynomials - Exercises Set 3.2 - Page 205: 18

Answer

$$ True. $$

Work Step by Step

True, if the derivative has one root at $ x = $ 1, then we know that the derivative does not have the same sign on the left and right of the root. According to the first derivative test, we then know that we have a relative extrema at $ x = 1$.
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