Thomas' Calculus 13th Edition

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

Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 240: 70

Answer

$\bf{Graph (b)}$

Work Step by Step

The anti-derivative for $\dfrac{dy}{dx}=-x$ is $y=-\dfrac{x^2}{2}+C$ Plug $x=1,y=1$ in above equation $y=-\dfrac{x^2}{2}+C$ for solving the value of $C$. Thus, $C=\dfrac{3}{2}$ Hence, $y=-\dfrac{x^2}{2}+\dfrac{3}{2}$; This shows that a $\bf{Graph (b)}$with a concave down parabola.
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