If f(X)=x ln x then f(x) attains minumum value at which one of the following points ?

Options

A. `x=e^(-2)`
B. `x=e`
C. `x=e^(-1)`
D. `x=2e^(-1)`

Explanation

Let `f(X)=xIn x`
`f'(x)=(x)/(x)+In x=1 +In x`
Put `f'(x)=0 rarr 1 + In x=0`
`rarr In x=-1 rarr x=e^(-1)`
Now `f''(x)=(1)/(x)`
`f''(x)|_(x=e^(-1))=(1)/(e-1)=e gt 0`