TS EAMCET · Maths · Application of Derivatives
The number of admissible values of obtained when the Lagrange's mean value theorem is applied for the function on is
- A 0
- B only one
- C infinite
- D finitely many
Answer & Solution
Correct Answer
(C) infinite
Step-by-step Solution
Detailed explanation
Given, f(x)=x ⇒f'(x)=1 Here, f(5)=5, f(2)=2 Apply LMVT in [2,5) f(5)-f(2)5-2=f'C ⇒5-25-2=f'C ⇒f'C=1 So, infinite values of C are possible.
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