The value of c prescribed by Lagrange’s mean value theorem, when f(x)=x2-4  ,a=2 and  b=3 is  

The value of c prescribed by Lagrange's mean value theorem, when f(x)=x2-4  ,a=2 and  b=3 is  

  1. A

    2.5

  2. B

    5

  3. C

    3

  4. D

    3 +1

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    Solution:

    Clearly f(x)=x24 is continuous on [2,3]  and 

    differentiable on (2, 3). So, by Lagrange's mean value 

    theorem there exists  c(2,3)  such that 

    f(c)=f(3)f(2)32 cc24=50 f(x)=x24f(x)=xx24 c2=5c24 4c2=20

     c=5

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