Calculus (3rd Edition)

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

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 10: 57


$$ x=\sqrt[3] 2.$$

Work Step by Step

The zeros of $f(x)=2- x^3$ can be obtained by putting $$2-x^3=0\Longrightarrow x=\sqrt[3] 2.$$ Since $f(-x)\neq -f(x)$ nor $f(-x)\neq f(x)$ then the function is not symmetric about the origin nor about the y-axis and it is decreasing on the interval $(-\infty,\infty)$. See the figure below.
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