Let f (x) Satisfy The Requirement Of Lagrange’s Mean Value Theorem In [0, 2]. If f (0) And     

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Question

Let f (x) satisfy the requirement of lagrange’s mean value theorem in [0, 2]. If f (0) and   

 

Solution

Correct option is

Let x Ïµ (0, 2). Since f (x) satisfies the requirements of lagrange’s mean value theorem in [0, 2]. So, it also satisfied in [0, x]. Consequently, there exists c Ïµ (0, x) such that     

                                  

  

  

Testing

SIMILAR QUESTIONS

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If the relation between subnormal SN and subtangent ST at any point S on the curve; by2 = (x + a)3 is p(SN) = q(ST)2, then find the value of p/q. 

Q2

 in which interval

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If f (x) = xα log x and f (0) = 0, then the value of ‘α’ for which Rolle’s theorem can be applied in [0, 1] is:

Q4

If abc be non-zero real numbers such that  

                                                                      

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Q5

 

Find c of the Lagrange’s mean value theorem for which

Q6

Let f (x) and g (x) be differentiable for 0 ≤ x ≤ 2 such that (0) = 2, g(0) = 1 and f (2) = 8. Let there exists a real number c in [0, 2] such that f’(c) = 3g’(c) then the value of g(2) must be:

Q7

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Q9

In [0, 1] lagrange’s mean value theorem is not applicable to

Q10

Let f : [2, 7] and [0, ) be a continuous and differentiable function.

Then the value of (f (7) – f (2))  is (where c Ïµ (2, 7))