Mark the correct alternative in the following:

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

Given:-

$f(x)=2 x^{3}-9 x^{2}+12 x+29$

$\frac{\mathrm{d}(\mathrm{f}(\mathrm{x}))}{\mathrm{dx}}=\mathrm{f}^{\prime}(\mathrm{x})=6(\mathrm{x}-1)(\mathrm{x}-2)$

for decreasing function $f^{\prime}(x)<0$

$f^{\prime}(x)<0$

$\Rightarrow 6(x-1)(x-2)<0$

$\Rightarrow 1