What I hope to do in this video is prove that if a function is differentiable at some point C, that it's also going to be continuous at that point C. But before we do the proof, let's just remind ourselves what differentiability means and what continuity means. So first, differentiability. Differentiability. So let's think about that first. It's always helpful to draw ourselves a function. So that's our y-axis. This is our x-axis.