Q. If $f(x)=-2 x^3+9 x^2+p x+20$ is an increasing function of $x$ in the largest interval $(-1,4)$ then $p$ is equal to
Application of Derivatives
Solution:
$ f ^{\prime}( x )=-6 x ^2+18 x + p >0 \forall x \in(-1,4)$
$=-6\left(x^2-3 x-\frac{p}{6}\right)$
Now, $\frac{-p}{6}=-4$
$\Rightarrow p=24$
