AP EAMCET · Maths · Differentiation
If \(3 f(x)-2 f\left(\frac{1}{x}\right)=x\) then \(f^{\prime}(2)=\)
- A 1
- B \(\frac{1}{2}\)
- C 2
- D \(\frac{7}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(3 f(x)-2 f\left(\frac{1}{x}\right)=x\)...(i) Replacing \(x\) by \(\frac{1}{x}\), we get \(3 f\left(\frac{1}{x}\right)-2 f(x)=\frac{1}{x}\)...(ii) Solving (i) and (ii), \(f(x)=\frac{1}{5}\left(3 x+\frac{2}{x}\right)\)…
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