The interval in which 2 x^3+5 increases less rapidly than 9 x^2-12 x,…

Let $f(x)=2 x^3+5$ and $g(x)=9 x^2-12 x$. Then, f(x) increases less rapidly than g(x) means that

$\frac{d}{d x}(f(x))<\frac{d}{d x}(g(x))$

$\Rightarrow \frac{d}{d x}(f(x)-g(x))<0$

$\Rightarrow f'(x)-g'(x)<0$

$\Rightarrow 6 x^2-(18 x-12)<0$

$\Rightarrow x^2-3 x+2<0$

$\Rightarrow x \in(1,2)$