Answer
$a\geq 0$
Work Step by Step
Given $$f(x)=x^{3}+a x+b$$
Since
$$f'(x) =3x^{2}+a$$
Since $3x^2\geq 0$, then the condition that guarantees $f'(x)>0$ is $a\geq 0$.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 4 - Applications of the Derivative - 4.3 The Mean Value Theorem and Monotonicity - Exercises - Page 190: 53
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