Now this is starting to get interesting. One way to think about it is there must be a c, if we, there must be a c that takes on the average value of, there must be a c that when you evaluate the derivative at c, it takes on the average value of the derivative. Or another way to think about it, another way to think about it, if we were to just write, if we were to just write, let me just say g of x is equal to f prime of x, then we get very close to what we have over here, because this right over here is going to be g of c. Remember, f prime of c is the same thing as g of c, is equal to one over, is equal to one over b minus a, one over b minus a. So there exists a c, where g of c is equal to one over b minus a, times the definite integral from a to b of g of x, g of x, dx. F prime of x is the same thing as g of x. So another way of thinking about it, and this is actually another form of the mean value theorem, it's called the mean value theorem for integrals. Mean value theorem for integrals.