If f(x)= { e^(-x)+2, for x<0

Question

{ ax+b, for x=>0
is differentiable at x=0, then a+b=_____?

Answer 1

My work

lim f(x) =3
x->0-

lim f(x) =b
x->0+

3=b

lim f'(x)=-1
x->0-

lim f'(x) =a
x->0+

a=-1

therefore a+b=2

AM I RIGHT?

Please help

Answer 2

looks good to me.