AP EAMCET · Maths · Differentiation
If \(3 f(x)-2 f\left(\frac{1}{x}\right)=x\), then \(f^{\prime}(2)\) is
- A \(\frac{7}{2}\)
- B \(\frac{1}{2}\)
- C \(\frac{2}{7}\)
- D 2
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(3 f(x)-2 f\left(\frac{1}{x}\right)=x, f^{\prime}(2)=\) ? \(\Rightarrow 3 f^{\prime}(x)-2 f^{\prime}\left(\frac{1}{x}\right)\left(-\frac{1}{x^2}\right)=1\) At \(\quad(x=2) \Rightarrow 3 f^{\prime}(2)+\frac{1}{2} f^{\prime}\left(\frac{1}{2}\right)=1\) ...(i) And At…
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