(1)

Step 1:

The function is  , .

Rolles theorem :

Let be a function that satisfies the following three hypotheses.

1. is continuous on .

2. is differentiable on .

3. .

Then there is a number  in  such that .

The function is continuous over , since it is a polynomial function. \ \

.

Substitute in the function.

.

Substitute in the function.

Therefore  .

Hence function satisfy the Rolles theorem.

There exist at least one  value in the interval ,such that .

Step 2: \ \

.

Differentiate on each side with respect to .

.

Equate it to zero.

Hence . \ \

The value of .

2)

Step 1:

The function is  , .

Rolles theorem :

Let  be a function that satisfies the following three hypotheses.

1.  is continuous on .

2.  is differentiable on .

3. .

Then there is a number  in  such that .

The function is continuous over and differentiable on , since it is a polynomial function. \ \

.

Substitute in the function.

.

Substitute in the function.

Therefore  .

Hence function satisfy the Rolles theorem.

There exist at least one  value in the interval ,such that .

Step 2: \ \

.

Differentiate on each side with respect to .

.

Equate it to zero.

and .

Hence and . \ \

The values of are .