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