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The number of nonzero integral values of...

The number of nonzero integral values of `a` for which the function `f(x)=x^4+a x^3+(3x^2)/2+1` is concave upward along the entire real line is___________

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Verified by Experts

The correct Answer is:
4
`f(x)=12x^(2)+6ax+3ge0forall x in R`
or `36a^(2)-144le0`
or `ain[-2,2]`
Thus number of nonzero integral values of a is 4
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CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Numerical)
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