question_answer

If \[f(x)=x\text{ }for\text{ }x\le 1,\text{ }f(x)={{x}^{2}}+bx+c\text{ }for\text{ }x>1\]and f'(x) exists finitely for all \[x\in \,R\], then

A)  \[b=-1.\,c\in R\]  

B)  \[c=1,\text{ }b\in R\]

C)  \[b=1,\text{ }c=-1\]   

D)  \[b\text{ }=-1,\text{ }c=\text{ }1\]