# Example 43

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 43 Verify Mean Value Theorem for the function ( ) = 2 in the interval [2, 4]. ( ) = 2 in interval [2, 4]. Checking conditions for Mean value Theorem Condition 1 = 2 is continuous at 2 , 4 Since ( ) is polynomial . it is continuous in 2 , 4 Condition 2 = 2 is differentiable in 2 , 4 Since is a polynomial . it is differentiable is defined 2 , 4 Now, = 2 & = 4 = 2 2 = 4 = 4 2 = 16 = 2 = 2 = 2 Now = 2 = 16 4 4 2 2 = 12 2 2 = 6 = 3 Value of c is 3 which lies between 2 and 4. Hence c = 3 , Hence, Mean value Theorem is satisfied .

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.