Problems on Fundamental Theorem-1:
3. Verify Rolle's Theorem for the functions.
Solutions:
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.
(i)
We have the Theorem
The theorem becomes,
Thus the Theorem is verified.