A) \[(-\infty ,\,-1)\]
B) (?5 , 1)
C) (?1 ,5)
D) (5 , \[\infty \])
Correct Answer: C
Solution :
The function \[f(x)={{x}^{3}}\]increases for all x and the function \[g(x)=6{{x}^{2}}+15x+5\]increases, if \[g'(x)>0\Rightarrow 12x+15>0\Rightarrow x>-\frac{5}{4}\]. Thus \[f(x)\] and \[g(x)\]both increases for \[x>-\frac{5}{4}\]. It is given that\[f(x)\]increases less rapidly than \[g(x)\], Therefore the function \[\varphi (x)=f(x)-g(x)\]is decreasing function , which implies that \[\varphi '(x)<0\] Þ \[3{{x}^{2}}-12x-15<0\Rightarrow -1<x<5\].You need to login to perform this action.
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