# Problems On Fundamental Theorem

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**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.