AP EAMCET · Maths · Application of Derivatives
The constant ' \(\mathcal{C}\) ' of Lagrange's mean value theorem for the function \(f(x)=\frac{2 x+3}{4 x-1}\) defined on \([1,2]\) is
- A \(\frac{1+\sqrt{15}}{3}\)
- B \(\frac{1+\sqrt{21}}{4}\)
- C \(\frac{5}{3}\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1+\sqrt{21}}{4}\)
Step-by-step Solution
Detailed explanation
Using mean value theorem, we have \[ \begin{aligned} f^{\prime}(c) & =\frac{f(2-f(1)}{2-1} \\ \Rightarrow \frac{-14}{(4 c-1)^2} & =\frac{1-\frac{5}{3}}{1} \end{aligned} \]…
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