Applications Of Derivatives Question 296
Question: The function $ x^{2}\log x $ in the interval (1, e) has
Options:
A) A point of maximum
B) A point of minimum
C) Points of maximum as well as of minimum
D) Neither a point of maximum nor minimum
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ f(x)=x^{2}\log x $
therefore $ f’(x)=2x\log x+x $ and $ {f}’’(x)=2(1+\log x)+1 $
Now $ {f}’’(1)=3+2{\log_{e}}1 $ and $ {f}’’(e)=3+2{\log_{e}}e $
$ f(x) $ has local minimum at $ \frac{1}{\sqrt{e}} $ , but $ x $ lies only in interval $ (1,e) $ so that $ y_2=\sqrt{x} $ has not extremum in $ (1,e). $
Hence neither a point of maximum nor minimum.
BETA
