By approximately matching the information given in the three columns of the following table.

Let f(x) = x + log_e x $-$ x log_e x, x $\in$(0, $\infty$)

Column 1 contains information about zeroes of f(x), f'(x) and f"(x).

Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.

Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).

	Column - 1	Column - 2	Column - 3
(i)	f(x) = 0 for some $x \in (1,{e^2})$	(i) $\mathop {\lim }\limits_{x \to \infty } \,f(x) = 0$	f is increasing in (0, 1)
(ii)	f'(x) = 0 for some $x \in (1,e)$	$$\mathop {\lim }\limits_{x \to \infty } \,f(x) = - \infty$$	f is decreasing in (e, ${e^2}$)
(iii)	f'(x) = 0 for some $x \in (0,1)$	$$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = - \infty$$	f' is increasing in (0, 1)
(iv)	f'(x) = 0 for some $x \in (1,e)$	$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = 0$	f' is decreasing in (e, ${e^2}$)

Which of the following options is the only CORRECT combination?