A) \[\left( \frac{1}{3},\,1 \right)\]
B) \[\left( -\frac{1}{3},1 \right)\]
C) \[\left( -\frac{1}{3},\,\frac{1}{3} \right)\]
D) \[\left( -1,-\frac{1}{3} \right)\]
Correct Answer: B
Solution :
Given \[f(x)={{x}^{3}}-{{x}^{2}}-x-4\] This function will be decreasing function when \[f'(x)<0\] Þ \[3{{x}^{2}}-2x-1<0\Rightarrow 3{{x}^{2}}-3x+x-1<0\] Þ \[(3x+1)(x-1)<0\]; \[\therefore 3x+1>0\]and \[x-1<0\] \[x>-\frac{1}{3}\]and \[x<1\] :\[\therefore x\in \left( \frac{-1}{3},\,1 \right)\] .You need to login to perform this action.
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