And then they say there's no point c between in that interval for which f prime of c is equal to the average rate of change. Explain why the statement does not contradict the mean value theorem. Fascinating. All right, let's do this first part first. The average rate of change of f on the interval. Sounds like a very fancy thing, but the average rate of change on the interval is really just the slope of the line that connects the endpoints of the interval. So this right over here, those are the endpoints, and let's figure out the slope of that line.