A) \[-7\]
B) 5
C) 7
D) 6
Correct Answer: C
Solution :
\[f'(x)=3{{x}^{2}}-6(a-2)x+3a\] |
\[f'(x)\ge 0\forall x\in (0,1]\] |
\[f'(x)\le 0\forall x\in [1,5)\] |
\[\Rightarrow \] \[f'(x)=0\]at \[x=1\]\[\Rightarrow \]\[a=5\] |
\[f(x)-14={{(x-1)}^{2}}(x-7)\] |
\[\frac{f(x)-14}{{{(x-1)}^{2}}}=x-7\] |
Hence, root of equation \[\frac{f(x)-14}{{{(x-1)}^{2}}}=0\,\]is 7. |
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