Examine the applicability of Mean Value Theorem for all the three functions being given below: [Note for students: Check exercise 2] (i) for

Solution:

(i) for ……….(1)

Provided here, is a polynomial function.

Then, is continuous and derivable on the real line.

Therefore is continuous in the closed interval and derivable in open interval .

As a result, both conditions of M.V.T. are satisfied.

From the equation (1), we have

Now again, from the equation (1):

And,

Then,

As a result, Mean Value Theorem is verified.