Limits Continuity And Differentiability Question 65
Question: Let $ 3f(x)-2f(1/x)=x, $ then $ f’(2) $ is equal to
Options:
A) $ \frac{2}{7} $
B) $ \frac{1}{2} $
C) $ 2 $
D) $ \frac{7}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ 3f(x)-2f( \frac{1}{x} )=x…(1) $
Put $ x=\frac{1}{x}, $
then $ 3f( \frac{1}{x} )-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}{5x^{2}} $
$ \therefore f’(2)=\frac{3}{5}-\frac{2}{20}=\frac{1}{2} $
BETA
