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: 20

Answer

Find an equation of the tangent line to the graph of $y = g(x)$ at $x = 5$ if $g(5) = -3$ and $g'(5) = 4$. $$y = 4x - 23$$

Work Step by Step

Find an equation of the tangent line to the graph of $y = g(x)$ at $x = 5$ if $g(5) = -3$ and $g'(5) = 4$. So, we are given a point on the equation $y = g(x)$, $(5, -3)$, and the derivative of $g(x)$ at that point, $4$, which is the same as the slope of the tangent line. Therefore, to find the equation of the tangent line, just plug these numbers into point slope form. Thus, we get $$y - 3 = 4(x-5)$$ After distributing and rearranging the terms, we get $$y = 4x - 23$$
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