And if you think about it, it's kind of intuitive that at some point, you know, here we're, we obviously have a larger slope, and over here we have a smaller slope. And since it's differentiable, our derivative is continuous. So at some point, at some point, the slope has to get to exactly what the average slope is. Now let's think about our little conundrum with this question right over here. Why is there not a point c for which f prime of c is equal to the average rate of change? And you can even verify that for yourself because from negative four to zero, our slope is positive. We have a positive slope here.