Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.1 Derivatives and Rates of Change - 2.1 Exercises - Page 114: 21


If an equation of the tangent line to the curve $y=f(x)$ at the point where $a=2$ is $y=4x - 5$, find $f(2)$ and $f'(2)$. $f(2)=3$ and $f'(2)=4$

Work Step by Step

The tangent line equation $y=4x - 5$ already tells us that $f'(2) = 4$ since the slope of the tangent is at 2 is $f'(2)$. To find $f(2)$, plug in $x=2$ to $y=4x - 5$. This yields $f(2)$ because at $x=2$, the y value of the tangent line is the same as the y value of $f(x)$. Thus, $f(2) = 3$.
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