Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.3 The Indefinite Integral - Exercises - Page 253: 63



Work Step by Step

$f’’(x)=12x,$ $f’(0)=1,$ $f(0)=2$ $f’(x)=\int12xdx$ $f’(x)=6x^2+C_1$ Substitute in $f’(0)=1$ to solve for $C_1$ $1=0+C_1$ $C_1=1$ $f(x)=\int(6x^2+1)dx$ $f(x)=2x^3+x+C_2$ Substitute in $f(0)=2$ to solve for $C_2$ $2=0+0+C_2$ $C_2=2$ $f(x)=2x^3+x+2$
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