Discussion Forum

The minimum value of the function f(x)= x log x is  

Answer:

Explanation:

We have ,

 f(x)= x log x

f'(x)= 1+log x

For maxima or minima , put f '(x)= 0

 $\therefore$    1+ log x=0

 $\Rightarrow$  logx =-1

 $\Rightarrow$  x = e^-1

 Now, f "(x) = $\frac{1}{x}$

 $\Rightarrow$    $f^{''}(e^{-1})=\frac{1}{e^{-1}}, e >0$

 $\therefore$ f(x) is decreasing

 Hence, minimum value of f(x) at x= e^-1 is

 $\Rightarrow$     $f^{}(e^{-1})=e^{-1}\log e^{-1}=\frac{1}{e}(-log e)=-\frac{1}{e}$