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: 20



Work Step by Step

To find the slope of a function at any given point, all one has to do would be to look for the value of the derivative function at the same x value. Given that $f(x)=x^3-2x+7$, then the derivative function by the power rule will be $f'(x)=3x^{3-1}-2x^{1-1}+7=3x^2-2$ As such, the slope at the point $x=-2$ would be $f'(-2)=3(-2)^2-2=10$
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