Question

If $f(x)=-2x^3+9x^2+px+20$ is an increasing function of $x$ in the largest interval $(-1,4)$ then $p$ is equal to

• A. 12
• B. 18
• C. 24
• D. -24

Answer 1

Answer: (C)

$f^{\prime }(x)=-6x^2+18x+p>0\forall x\in (-1,4)$
$=-6\left(x^2-3x-\frac{p}{6}\right)$
Now, $\frac{-p}{6}=-4$
$\Rightarrow p=24$