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.
Great explanation of the theorem, Jesus. Can you be a bit more specific though by showing the actual equations of the function and the slope of the tan/sec line?
ReplyDeleteAs for the second part, can you add a discontinuous example in there as well?
Very blunt ! :]
ReplyDeleteHowever, I would like to know a little more about each, like specifically why...
can you explain why it fails please.
ReplyDeleteits very general
more deets please :)
you should explain further more why the function has to be differentiable and continuous within the closed intervals
ReplyDelete