Well if we assume that f is differentiable at C, and we're going to do that, actually I should have started off there. Let's assume, let's assume, because we wanted to show that differentiability improves continuity. If we assume f differentiable, differentiable at C, well then this right over here is just going to be f prime of C. This right over here, we just saw it right over here, that's this exact same thing. This is f prime, f prime of C. And what is this thing right over here? The limit as x approaches C of x minus C? Well that's just going to be zero. As x approaches C, it's going to approach C minus C, it's just going to be zero.