ExamBro
ExamBro
AP EAMCET · Maths · Differentiation

If \(3 f(x)-2 f\left(\frac{1}{x}\right)=x\), then \(f^{\prime}(2)\) is

  1. A \(\frac{7}{2}\)
  2. B \(\frac{1}{2}\)
  3. C \(\frac{2}{7}\)
  4. D 2
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{1}{2}\)

Step-by-step Solution

Detailed explanation

\(3 f(x)-2 f\left(\frac{1}{x}\right)=x, f^{\prime}(2)=\) ? \(\Rightarrow 3 f^{\prime}(x)-2 f^{\prime}\left(\frac{1}{x}\right)\left(-\frac{1}{x^2}\right)=1\) At \(\quad(x=2) \Rightarrow 3 f^{\prime}(2)+\frac{1}{2} f^{\prime}\left(\frac{1}{2}\right)=1\) ...(i) And At…