AP EAMCET · Maths · Application of Derivatives
For \(m > 1, n > 1\), the value of \(c\) for which the Rolle's theorem is applicable for the function \(f(x)=x^{2 m-1}(a-x)^{2 n}\) in \((0, a)\) is
- A \(\frac{2 a m-1}{m+2 n-1}\)
- B \(\frac{a(m-n+1)}{2 m+2 n}\)
- C \(\frac{a(2 m-1)}{2 m+2 n-1}\)
- D \(\frac{a(2 m+1)}{m+n-1}\)
Answer & Solution
Correct Answer
(C) \(\frac{a(2 m-1)}{2 m+2 n-1}\)
Step-by-step Solution
Detailed explanation
Since it is given that Rolle's theorem is applicaple for the function \(f(x)=x^{2 m-1}(a-x)^{2 n}\) in \((0, a). \)…
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