question_answer

The set of points where \[f(x)={{(x-1)}^{2}}(x+|x-1|)\] is thrice differentiable, is

A) \[R\]                            

B) \[R-\{0\}\]

C) \[R-\{1\}\]                   

D) \[R-\{0,\,\,1\}\]

Correct Answer: C

Solution :

 Since \[|x|\] is not diff. at\[x=0\] \[\Rightarrow \]\[|x-1|\]is not diff at\[x=1\].\[{{x}^{n}}|x|\]in\[n\]times diff. at\[x=0\] \[\Rightarrow \]\[{{(x-1)}^{2}}|x-1|\]is twice diff. at\[x=1\]but not thrice diff. at\[x=1\]