So if we assume f is differentiable at C, we can write, we can write the limit, I'm just rewriting it, the limit as x approaches C of f of x minus f of C, and I could even put parentheses around it like that, which I already did up here, is equal to zero. Well this is the same thing, I could use limit properties again, this is the same thing as saying, and I'll do it over here, actually let me do it down here. The limit as x approaches C of f of x minus the limit as x approaches C of f of C, of f of C, is equal to zero. The limit of the difference is the same thing as the difference of the limits. Well what's this thing over here going to be? Well f of C is just a number, it's not a function of x anymore, it's just f of C is going to evaluate to something. So this is just going to be f of C. This is just going to be f of C. So if the limit of f of x as x approaches C minus f of C is equal to zero.