Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.1 Exercises: 47

Answer

$g(4)=5, g'(4)=-\frac{5}{3}$

Work Step by Step

$g(4)=5$ is given, since the problem specifies that the tangent line passes through the point $(4,5)$ and that $(4,5)$ is on the graph of $y=g(x)$. Therefore, $g(4)=5$. To find $g'(4)$, find the slope of the tangent line using the other given point $(7,0)$: $g'(4)=\frac{0-5}{7-4}=-\frac{5}{3}$
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