JEE Main & Advanced
Sample Paper
JEE Main Sample Paper-38
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\[x=1\]