differentiability doubt

[Xiang]

f(x)= 1/lxl for lxl>=1
         ax^2+b for lxl<1

if f(x) is continuous and differentiable. find a and b.

I have a problem in the limits! Please help.

Thank you

[Sinistral]

f(x) = -1/x,           x ≤ -1
          ax^2 +b , -1<x<1
          1/x ,          x≥ 1

since it is continuous f(1- ɛ)=f(1+ ɛ)  where  ɛ is a very small positive number.
so a+b = 1

since it is derivable f'(1- ɛ)=f'(1+ ɛ)  where  ɛ is a very small positive number.
2ax =  -1/x^2  (at x=1)
a=-1/2
hence, b=3/2

[Xiang]

Oh thank you so much!