Well, this is useful, because this is exactly what we got as the derivative of f prime of x. So there must exist a c such that f of c is equal to this stuff, or we could say that the limit, and let me rewrite all of this down a new color. So there exists a c in the interval x to x plus delta x, where f prime of x, which we know is equal to this, we can now say is now equal to the limit as delta x approaches 0. And instead of writing this, we know that there's some c that's equal to all of this business, of f of c. Now we're in the home stretch. We just have to figure out what the limit as delta x approaches 0 of f of c is. And the main realization is this part right over here. We know that c is always sandwiched in between x and x plus delta x.