Mark the correct alternative in the following:

Formula:- (i) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on $(a, b)$ is that $f^{\prime}(x)>0$ for all $x \in(a, b)$

Given:-

$f(x)=x^{3}-27 x+5$

$\frac{d(f(x))}{d x}=3 x^{2}-27=f^{\prime}(x)$

for increasing function $f^{\prime}(x)>0$

$3 x^{2}-27>0$

$\Rightarrow(x+3)(x-3)>0$

$\Rightarrow|x|>3$