University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Section 4.2 - The Mean Value Theorem - Exercises - Page 223: 33

Answer

a) $y=\dfrac{x^2}{2}+C$ b) $y=\dfrac{x^3}{3}+C$ c) $y=\dfrac{x^4}{4}+C$

Work Step by Step

a) When $x=(\dfrac{x^2}{2})'$ Thus, $y'=x \implies y=\dfrac{x^2}{2}+C$ b) When $x=(\dfrac{x^3}{3})'$ Thus, $y'=x^2 \implies y=\dfrac{x^3}{3}+C$ c) When $x=(\dfrac{x^4}{4})'$ Thus, $y'=x^3 \implies y=\dfrac{x^4}{4}+C$
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