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. At every point in its domain. The closed interval from one to two is in domain. And so now let's see what the average rate of change is from one to two. And so we get g of two minus g of one over two minus one is equal to 1 1⁄2 minus one over one, which is equal to negative 1 1⁄2. Therefore, therefore, by the mean value theorem, there must be a c where one is less than c is less than two and g prime of c is equal to the average rate of change between the endpoints, negative 1 1⁄2. And we're done.