Now why is this interesting? Well we just said, we just assumed that if f is differentiable at C, and we evaluate this limit, we get zero. 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?