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
Correct Answer: D
Solution :
Let\[f(x)={{x}^{2}}\log x\]Þ\[f'(x)=2x\log x+x\] 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.
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