A) \[{{(x-1)}^{2}}\]
B) \[{{(x-1)}^{3}}\]
C) \[{{(x+1)}^{3}}\]
D) \[{{(x+1)}^{2}}\]
Correct Answer: B
Solution :
\[f\,(x)=6(x-1)\] \[\Rightarrow \] \[f(x)=3{{(x-1)}^{2}}+c\] ...(i) At the point (2,1) the tangent to graph is \[y=3x-5.\] Slope of tangent \[=3\Rightarrow f(2)=3\] \[\therefore \] \[f(2)=3{{(2-1)}^{2}}+c=3\] \[\Rightarrow \] \[3+c=3\Rightarrow c=0\] \[\therefore \]From Eq. (i) \[f(x)=3{{(x-1)}^{2}}\] \[\Rightarrow \] \[f(x)={{(x-1)}^{3}}+k\] ....(ii) Since graph passes through (2,1) \[\therefore \] \[1={{(2-1)}^{2}}+k\] \[k=0\] \[\therefore \]Equation of function is \[f(x)={{(x-1)}^{3}}\]You need to login to perform this action.
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