A) \[f(x)\]is continuous but not differentiable at \[x=0\]
B) \[f(x)\] is differentiable at \[x=0\]
C) \[f(x)\]is not differentiable at \[x=0\]
D) none of these
Correct Answer: C
Solution :
Here \[f(x)=x(\sqrt{x}+\sqrt{x+1})\] \[\Rightarrow \]\[f(x)\]would exist when \[x\ge 0\]and \[x+1\ge 0\] \[\Rightarrow \]\[f(x)\] would exist when \[x\ge 0.\] \[\therefore \] Domain of \[f(x)\] is \[(0.,\infty ).\] Hence, \[f(x)\]is not differentiable at \[x=0.\]
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