A) \[\frac{2}{7}\]
B) \[\frac{1}{2}\]
C) \[2\]
D) \[\frac{7}{2}\]
Correct Answer: B
Solution :
[b] \[3f(x)-2f\left( \frac{1}{x} \right)=x...(1)\] Put \[x=\frac{1}{x},\] then \[3f\left( \frac{1}{x} \right)-2f(x)=\frac{1}{x}...(2)\] Solving (1) and (2), we get \[5f(x)=3x+\frac{2}{x}\Rightarrow f'(x)=\frac{3}{5}-\frac{2}{5{{x}^{2}}}\] \[\therefore f'(2)=\frac{3}{5}-\frac{2}{20}=\frac{1}{2}\]
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