Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.1 - Tangents and the Derivative at a Point - Exercises 3.1 - Page 108: 4

Answer

See figure, $3$ and $-3$

Work Step by Step

At point $P_1$, draw a tangent line to the curve as shown in the figure. We can identify two points on the line $(-2, 0.33)$ and $(-1, 3.33)$; thus the slope of the line can be found as $m_1=\frac{3.33-0.33}{-1+2}=3$. At point $P_2$, draw a tangent line to the curve as shown in the figure. We can identify two points on the line $(2, 0.33)$ and $(1, 3.33)$; thus the slope of the line can be found as $m_2=\frac{3.33-0.33}{1-2}=-3$.
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