question_answer

The value of k: if  is both continuous and differentiable for all \[x\in R\] is

A) \[-1/2\]                 

B)        \[0\]                    

C) \[1/2\]                  

D)        None of these

Correct Answer: D

Solution :

[d] \[f(x)\]is continuous at\[x=1\]. \[\therefore \,\,\,\,\,f({{1}^{-}})=f({{1}^{+}})\] \[\Rightarrow \,\,\,\,\,\,3-2k-2=0\] \[\Rightarrow \,\,\,\,\,\,\,k=\,{{\,}^{\frac{1}{2}}}\] Clearly, \[f(x)\] is not differentiable at\[x=1\].