Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.1 - Tangents and the Derivative at a Point - Exercises 3.1 - Page 108: 25



Work Step by Step

Given that $f(x)=x^2+4x-1$, the function will have a horizontal tangent when the derivative is equal to 0, since the slope will indicate that there is no change in the y value of the tangent when x changes. $f'(x)$ is found using the power rules: $f'(x)=2x+4$ We let $f'(x)$ be equal to zero. $2x+4=0$ $x=-2$ $f(-2)=-5$ Thus, at the point $(-2,-5)$, there is maximum or a minimum where the graph will have a horizontal tangent.
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