- The mean value theorem means that the graph is continuous , differentiable and defined thoughout the function. The graph shows two parallel lines that are passing through points [a, f(a)] and [b , f(b)]. The theorem states that within [a,b] , there is a point where the slope of the parallel lines are the same.
The graph shows a jump discontinuity and a corner .
( I used Eric's example )
The function is on the interval of [0,7] and shows a discontinuous function. It is clearly shown that
points A to B has a slope that is not parallel to the rest of the function. Points C to D show a corner discontinuity.
This shows that when X=5 there is a corner. and the slope of the line between C to D is =0 , therefore Undefined. Since the slope of each
portion [a,b] and [c,d] are different slopes , the Mean Theorem cannot apply to a discontinuous function because their isnt a point where the slope of the differential function is equivalent to the derivative .
hey we used the same graph to prove the Mean Value Theorem graphically.Good explanation!
ReplyDeleteMs. Hwang !! You take forever :O lol xD
ReplyDeletehaha. so sorry Davis!
ReplyDeleteOk, you need specific functions for the first part. Equations for all 3 curves/lines.
As for the second part, you seem to be defining what a discontinuity and non differentiability is, but you're not saying why the Mean Value Thm doesnt work for it. Not only that, if in that graph you're talking about the interval [0,7], there IS a tangent line that is parallel to the secant line- anywhere the slope is 0!
am i done yet?(dont answer) i mean it......... no pun intended
ReplyDeletethe last graph was good
ReplyDeletekilled to birds with one stone!