Applications Of Derivatives Question 56
Question: If $ f(x)=x\ell nx $ , then $ f(x) $ attains minimum value at which one of the following points-
Options:
A) $ x={e^{-2}} $
B) $ x=e $
C) $ x={e^{-1}} $
D) $ x=2{e^{-1}} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Let $ f(x)=xlnx $
$ f’(x)=\frac{x}{x}+ $ ln $ x=1+lnx $ Put $ f(x)=0\Rightarrow 1+lnx=0 $
$ \Rightarrow $ ln $ x=-1\Rightarrow x={e^{-1}} $ Now, $ f’’(x)=\frac{1}{x} $
$ f’’(x)| _{x=e}-1=\frac{1}{{e^{-1}}}=e>0 . $
Hence, $ f(x) $ attains minimum value at $ x={e^{-1}} $ .
BETA
