Good job ndiggity, you're almost there, and everything you have done so far is on the right track.

All you need to do now is find the value of x for which f'(x) = -1. This must be the point at which x+y=0 is a tangent, as the derivative is the same there. You can then get the y value for that point from x+y = 0 then solve your other equation for C.