Question:
The maximum value of $y = x(\log x)^2$ is:
The maximum value of $y = x(\log x)^2$ is:
Show Hint
Always verify maxima using second derivative test.
Updated On: Jun 10, 2026
- $e^{-2}$
- $2e^{-2}$
- $4e^{-2}$
- $5e^{-2}$
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The Correct Option is C
Solution and Explanation
\[
y' = 2\log x + (\log x)^2
\]
\[
\log x(2+\log x)=0
\]
\[
x=1,\ e^{-2}
\]
Maximum at $x=e^{-2}$:
\[
y = 4e^{-2}
\]
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