All right, let's do the second part. Can we use the mean value theorem to say that there is a value c such that g prime of c is equal to negative 1 1 2 and one is less than c is less than two? If so, write a justification. So pause the video again. All right, so in this situation, between one and two on both the open and the closed intervals, well, this is a rational function and a rational function is going to be continuous and differentiable at every point in its domain and its domain completely contains this open and closed interval. Or another way to think about it, every point on this open interval and on the closed interval is in the domain. So we can write g of x is a rational function which lets us know that it is continuous and differentiable at every point in its domain.