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 - Page 114: 23

Answer

The curve has a slope of$ −1 $ as we pass over $x$ = $2$. Two of the many possibilities.

Work Step by Step

We begin by drawing a curve through the origin with a slope of $3$ to satisfy $f(0)$ = $0$ and $f'(0)$ =$3$ . Since $f'(1)$ =$ 0$, we will round off our figure so that there is a horizontal tangent directly over$ x$ = 1. Last, we make sure that the curve has a slope of$ −1 $ as we pass over $x$ = $2$. Two of the many possibilities.
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