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: 48

Answer

$h(-1)=4, h'(-1)=\frac{1}{2}$

Work Step by Step

$h(-1)=4$ is given, since the problem specifies that the tangent line passes through the point $(-1,4)$ and that $(-1,4)$ is on the graph of $y=h(x)$. Therefore, $h(-1)=4$. To find $h'(-1)$, find the slope of the tangent line using the other given point $(3,6)$: $h'(-1)=\frac{6-4}{3-(-1)}=\frac{2}{4}=\frac{1}{2}$
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