Applications Of Derivatives Question 260
Question: The function $ f(x)=\frac{\log x}{x} $ is increasing in the interval
[UPSEAT 2001]
Options:
A) $ (1,,2e) $
B) (0,e)
C) (2, 2e)
D) (1/e, 2e)
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x)=\frac{\log x}{x} $
$ {f}’(x)=\frac{1}{x^{2}}-\frac{\log x}{x^{2}}=\frac{1-\log x}{x^{2}} $ For $ f(x) $ to be increasing, $ {f}’(x)>0 $
therefore $ 1-\log x>0 $
therefore $ 1>\log x $
therefore $ e>x $ \ $ f(x) $ is increasing in the interval $ (0,,e) $ .
BETA
