The interval in which the function 2 ^ 3 +15 increases less rapidly...

Let $f(x)=2 x^{3}+15$ and $g(x)=9 x^{2}-12 x$ then $\mathrmf^{\prime}(\mathrm{x})=6 \mathrmx^{2} \forall \mathrm{x} \in \mathrm{R}\therefore \mathrm{f}(\mathrm{x})$ is increasing function $\forall \mathrm{x} \in \mathrm{R}\text{ Also, }$ g^{\prime}(x)>0 \Rightarrow 18 x-12>0 \Rightarrow x>$\frac{2}{3}$ Thus, $\mathrm{f}(\mathrm{x})$ and $\mathrm{g}(\mathrm{x})$ both increases for $\mathrm{x} > \frac{2}{3}\text{ Let }$ F(x)=f(x)-g(x), F^{\prime}(x)<0 $(\because \mathrm{f}(\mathrm{x})$ increases less rapidly than the function $\mathrm{g}(\mathrm{x})) \Rightarrow 6 \mathrmx^{2}-18 \mathrm{x}+12<0 \Rightarrow 1<\mathrm{x}$<2