Mark the correct alternative in the following:

Formula:- (i) $a x^{2}+b x+c>0$ for all $x \Rightarrow a>0$ and $b^{2}-4 a c<0$

(ii) $a x^{2}+b x+c<0$ for all $x \Rightarrow a<0$ and $b^{2}-4 a c<0$

(iii) 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:-

$f(x)=x^{3}-9 k x^{2}+27 x+30$

$\frac{\mathrm{d}(\mathrm{f}(\mathrm{x}))}{\mathrm{dx}}=\mathrm{f}^{\prime}(\mathrm{x})=3 \mathrm{x}^{2}-18 \mathrm{kx}+27$

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

$3 x^{2}-18 k x+27>0$

$\Rightarrow x^{2}-6 k x+9>0$

Using formula (i)

$36 k^{2}-36>0$

$\Rightarrow K^{2}>1$

Therefore $-1