Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 103: 22


$$ f'(3)=5, \quad f(3)=17.$$

Work Step by Step

Since the tangent line at $ x=3, $ has the equation $$ y=5x+2,$$ then $ f'(3)$ is the slope, that is, $$ f'(3)=5.$$ Moreover, the tangent line at $ x=3$ coincides with the function itself, that is, $$ f(3)=5(3)+2=15+2=17.$$
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