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

$(-\infty, 1)$ $(1,2)$ $(2, \infty)$ none of these

$(1,2)$

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 $\frac{d}{d x}(f(x))<\frac{d}{d x}(g(x))$ $\Rightarrow \frac{d}{d x}(f(x)-g(x))<0$ $\Rightarrow f'(x)-g'(x)<0$ $\Rightarrow 6 x^2-(18 x-12)<0$ $\Rightarrow x^2-3 x+2<0$ $\Rightarrow x \in(1,2)$