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Q.
The set of values of ' $x$ ' for which function $f(x)=x \ln x-x+1$ takes positive value only, is
Application of Derivatives
Solution:
$ f ( x )= x \ln x - x +1 ; f (1)=0$
$f ^{\prime}( x )=1+\ln x -1=\ln x $
$f ^{\prime}( x )=$
$\Rightarrow f ( x ) \text { is decreasing for }(0,1) \text { and increasing for }(1, \infty)$
$f ( x )_{\min }= f (1)=0 $
$f ( x ) \geq 0 \forall x \in(0, \infty)$
