A) \[{{(x-1)}^{2}}\]
B) \[{{(x-1)}^{3}}\]
C) \[{{(x+1)}^{3}}\]
D) \[{{(x+1)}^{2}}\]
Correct Answer: B
Solution :
We have, \[f''\,(x)=6x-6\] On integrating, we get \[f'(x)=3{{x}^{2}}-6x+c\] At \[x=2,\] \[f'(2)=3\] \[\Rightarrow \] \[12-12+c=3\] \[\Rightarrow \] \[c=3\] \[\therefore \] \[f'(x)=3{{x}^{2}}-6x+3\] Again integrating we get \[f(x)={{x}^{3}}-3{{x}^{2}}+3x+d\] when \[x=2,\,\,y=1\] \[f(2)=1={{(2)}^{3}}-3{{(2)}^{2}}+3(2)+d\] \[\Rightarrow \] \[d=-1\] \[\therefore \] \[f(x)={{x}^{3}}-3{{x}^{2}}+3x-1\] \[={{(x-1)}^{3}}\]You need to login to perform this action.
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