Question

If $y=x^3-a{x}^2+48x+7$ is an increasing function for all real values of $x,$ then a lies in:

• A. $(-14,14)$
• B. $(-12,12)$
• C. $(-16,16)$
• D. $(-21,21)$
• E. $(0,a)$

Answer 1

Answer: (B)

$\frac{dy}{dx}=3x^2-2ax+48>0$ ( $\because$ y is an increasing function) $\therefore$ Discriminant, $D<04a^2-4\times 3\times 48<0$ $\Rightarrow$ $a^2-144<0\Rightarrow a\in (-12,12)$