
Increasing/Decreasing
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 $\displaystyle 0<x<e^{\frac{3}{2}}$

Consider the graph of ln(x)