A) 0
B) 1
C) 2
D) more than 2
Correct Answer: B
Solution :
[b]: Let function is differentiable in R, then it will be differentiable at x = a. [\[\because \]Possible point of non-differentiability is x = a] \[f'({{a}^{+}})=\underset{h\to {{0}^{+}}}{\mathop{\lim }}\,\frac{(a+h+1)|h|-0}{h}=a+1\] \[{f}'({{a}^{-}})=\underset{h\to {{0}^{+}}}{\mathop{\lim }}\,\frac{(a-h+1)|-h|}{-h}=-\ (a+1)\] Now,\[f'({{a}^{+}})=f'({{a}^{-}})\Rightarrow a=-1\]
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