In this video, I explained the concept of Mean Value Theorem using a Polynomial. The instantaneous rate of change at 'c' is equal to the average rate of change.
Is it possible that the two points could be so close that there's no point (c) between them with the same gradient of the line joining the points? I am not certain that there should always be such a point (c).
As long b is not equal to a , there will always be a c between. You might think the points are close but when you zoom in , there are infinitely many points between two boundary points. As long as the function is continuous and differentiable over the interval.
