#### 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 $a\geq 0$.

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Published by
W. H. Freeman

ISBN 10:
1464125260

ISBN 13:
978-1-46412-526-3

$a\geq 0$

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