# NCERT Class 12-Mathematics: Chapter –5 Continuity and Differentiability Part 24

## Verify Mean Value Theorem for Each of the Functions Given Exercises 73 to 76

Question 73:

We have,

(i) is continuous in

Also, at is discontinuous

Hence, is continuous in .

(ii) which exists in ,

Since, conditions of mean value theorem are satisfied,

Hence, there exists a real number such that

Hence, mean value theorem has been verified.

Question 74:

(i) Since, is a polynomial function.

Hence, is continuous in

Hence, is differentiable in

Since, continuous of mean value theorem are satisfied, Therefore, by mean value theorem such that

Hence, the mean value theorem has been verified.

Question 75:

.

We have, .

(i) Since, we know that sine functions are continuous functions hence

is a continuous functions in

(ii) . Which exists in

So, is differentiable in . Continuous of mean value theorem are satisfied

Hence, such that,

Also,

Hence, mean value theorem has been verified.

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