Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - Chapter 2 Review Exercises - Page 184: 12

Answer

$f(x) = x^2+1$

Work Step by Step

For $f(0)=1$, the constant term of $f(x)$ must be $1$. Because $f'(0)=0$, there exists either a relative maximum or minimum at $x=0$. Because $f'(x)>0$ if $x<0$ and $f'(x)<0$ if $x>0$, the graph is then concave up and $x=0$ is a relative maximum. Thus, we can use the function $f(x) = x^2+1$ which satisfied all of these conditions.
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