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The set of values of ‘ $a$ ’ for which $f (x) = x^{3} - a x^{2} + 48 x + 1$ is increasing for all real values of ‘x’ is

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(–12, 12)

$(- \infty, - 12)$

$(12, \infty)$

$(- \infty, \infty)$

answer is A.

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$f^{'} (x) > 0 in that Δ < 0$ then $a \in (- 12, 12)$

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