Differentiation Question 17
Question: Let $ 3f(x)-2f(1/x)=x, $ then $ f’(2) $ is equal to
[MP PET 2000]
Options:
A) $ 2/7 $
B) $ 1/2 $
C) 2
D) $ 7/2 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ 3f(x)-2f(1/x)=x $
…..(i) Let $ 1/x=y $ , then $ 3f(1/y)-2f(y)=1/y $
Therefore $ -2f(y)+3f(1/y)=1/y $
Therefore $ -2f(x)+3f(1/x)=1/x $ …..(ii) From 3 × (i) + 2 × (ii), $ 9f(x)-6f(1/x)-4f(x)+6f(1/x)=3x+2/x $
$ 5f(x)=3x+\frac{2}{x} $
Therefore $ f(x)=\frac{1}{5}[ 3x+\frac{2}{x} ] $
Therefore $ f’(x)=\frac{1}{5}[ 3-\frac{2}{x^{2}} ] $
Therefore $ {f}’(2)=\frac{1}{5}[ 3-\frac{2}{4} ]=\frac{1}{2} $ .
BETA
