Find the values of b and c

Question

If f(x)=​​​​​

x ; x less than or equal to 1 

x^2 + bx+c ;    x>1 

Find the values of b and c if f(x) is differentiable at x=1

Comments

firstly,
if x<1 f(x)=x=1(x->1)
differentiate the function,
you get,
left hand side, f'(x)=d/dx(x)=1
right hand side, f'(x)=d/dx{x^2+bx+C)}
                                f'(x)=2x+b    =>f'(1)=2+b
LHS=RHS      =>   2+b=1  => b=-1
  f(x<1)=f(x>1)   x->1
    1=1+(-1)(1)+c
     1=c