So local linearity is this idea that if we zoom in sufficiently on a point, that even a nonlinear function that is differentiable at that point will actually look linear. So let me show some examples of that. So let's say we had y is equal to x squared. So that's that there, clearly a nonlinear function. But we can zoom in on a point and if we zoom sufficiently in, we will see that it looks roughly linear. So let's say we want to zoom in on the point one comma one. So let's do that.