Show that when the mean value theorem is applied to any interval [a, b], the point c which satisfies the conclusion of the theorem is the midpoint of the interval
The proposition stated here cannot be shown in general, because it is not true in general.
Consider the attached, which shows that over the interval [0, 4] for function f(x) = x(x-4)² the value of c that satisfies the theorem is c=4/3, which is not the midpoint of the interval.
