Problems On Fundamental Theorem

Problems on Fundamental Theorem-1:

3. Verify Rolle's Theorem for the functions.




f ' (x) exists in (a,b)

Also f (a) = 0 = f (b)

Hence all the condition of the theorem are satiesfied.

Now consider f ' (c) = 0


a.b are the end points.

is the x coordinate of the point which divides the line joining [a, f (a)], [b, f (b)] internally in the ratio m : n

Thus the Rolle's Theorem is verified.


We have the Theorem


The theorem becomes,


Thus the Theorem is verified.