For x>0, f is a function that

$\displaystyle f'(x)=\frac{\ln x}{x},\;\; f''(x)=\frac{1-\ln x}{x^2}$

Which of the following is true?

(a) f is decreasing for x>1, and graph of f is concave down for x>e

(b) f is decreasing for x>1, and graph of f is concave up for x>e

(c) f is increasing for x>1, and graph of f is concave down for x>e

(d) f is increasing for x>1, and graph of f is concave up for x>e

(e) f is increasing for 0<x<e, and graph of f is concave down for $\displaystyle 0<x<e^{\frac{3}{2}}$