The mean Value Theorem states that for a function to have a tangent line parallel a chord AB then it must be continuous at the interval [a,b],where the chord is located.
Algebraically speaking it means this: f'(c)= f(b)-f(a)/(b-a)
Algebraically speaking it means this: f'(c)= f(b)-f(a)/(b-a)
Graphically it looks like this:
Instances when the mean value theorem fails to work are when the graph is either not continuous or not differentiable on the interval that the chord is located
The graph above is not differentiable between the intervals that the chord is located therefore it has no tangent line parallel to ab.
