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Q.
For what value of $x, x^2 \ell n(1 / x)$ is maximum-
Application of Derivatives
Solution:
$f(x)=x^2 \ell n\left(\frac{1}{x}\right)=-x^2 \ell \ln x$
$f^{\prime}(x)=-[2 x \ell \ln x+x]=-x(2 \ln x+1)$
$\Rightarrow$ maximum at $x=\frac{1}{\sqrt{ e }}$
