So the slope between the two endpoints is gonna be your change in y, which is going to be your change in your function value, so f of b minus f of a over, over b minus a. And once again, we do this, we go into much more depth in this when we covered it the first time in differential calculus, but just to give you a visualization of it, because I think it's always handy, the mean value theorem that we learned in differential calculus just tells us, hey look, you know, if this is a, this is b, I've got my function doing something interesting, so this is f of a, this is f of b, so this quantity right over here, where you're taking the change in the value of our function divided by, so this right over here is f of b, f of b minus f of a is this change in the value of our function divided by the change in our x-axis, so it's our change in y over change in x, that gives us the slope, this right over here gives us the slope of this line, the slope of the line that connects, that connects these two points, that's this quantity, and this, the mean value theorem tells us that there's some c in between a and b where you're gonna have the same slope, so it might be at least one place, so it might be right over there where you have the exact same slope, there exists a c where the slope of the tangent line at that point is going to be the same, so this would be a c right over there, and we actually might have a couple of c's, that's another candidate c, there's at least one c where the slope of the tangent line is the same as the average slope across the interval, and once again, we have to assume that f is continuous and f is differentiable. Now, when you see this, it, something might, it might evoke some similarities with what we saw when we saw the, how we defined, I guess you could say, or the formula for the average value of a function. Remember, what we saw for the average value of a function, we said the average, the average value of a function is going to be equal to one over b minus a, notice, one over b minus a, you have a b minus a in the denominator here, times the definite integral from a to b of f of x dx. Now, this is interesting, because here we have a derivative, here we have an integral, but maybe we could connect these, maybe we could connect these two things. Well, one thing that might jump out at you is maybe we could rewrite, maybe we could rewrite this numerator right over here in this form somehow, and I encourage you to pause the video and see if you can, and I'll give you actually a quite huge hint, instead of it being an f of x here, what happens if there's an f prime of x there? So I encourage you to try to do that.