Calculus (3rd Edition)

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

Chapter 4 - Applications of the Derivative - Chapter Review Exercises - Page 222: 41


$x= 4/3$

Work Step by Step

Given $$y=x^{3}-4 x^{2}+4 x $$ Since \begin{align*} y'&=3x^{2}-8x+4 \\ y''&=6x-8 \end{align*} Then $f''(x)=0$ for $x=4/3$ and $$ y''>0\ \ \text{ for } \ x>4/3\\ y''<0\ \ \text{ for } \ x<4/3$$ Hence, there exists an inflection point at $x= 4/3$
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