A) \[(-\infty ,1)\]
B) \[(1,2)\]
C) \[(2,\infty )\]
D) None of these
Correct Answer: B
Solution :
Let \[f(x)=2{{x}^{3}}+15\] and \[g(x)=9{{x}^{2}}-12x\]then |
\[f'(x)=6{{x}^{2}}\,\forall \,x\in R\] |
\[\therefore \,\,f(x)\] is increasing function \[\forall \,x\in R\] |
Also, \[g'(x)>0\Rightarrow 18x-12>0\Rightarrow x>\frac{2}{3}\] |
Thus, \[f(x)\] and \[g(x)\] both increases for \[x>\frac{2}{3}\] |
Let \[F(x)=f(x)-g(x),\] \[F'(x)<0\] |
(\[\because \] \[f(x)\] increases less rapidly than the function g \[(x)\]) |
\[\Rightarrow \,\,6{{x}^{2}}-18x+12<0\] |
\[\Rightarrow \,\,\,1<x<2\] |
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