Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.7 - Derivatives and Rates of Change - 2.7 Exercises: 21

Answer

$f'(2)=4$ and $f(2)=3$

Work Step by Step

The equation of the tangent line $l$ to the curve $y=f(x)$ at the point where $a=2$ is $$(l):y=4x-5$$ Since $f'(2)$ is the slope of the tangent line $l$, we can deduce that $f'(2)=4$ (Remember that in a line equation $y=ax+b$, $a$ is the slope of that line) The point where $a=2$ also lies in the line $l$, therefore we can use its equation to find $f(2)$. At $a=2$, we have $$f(2)=4\times2-5=3$$
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