Question

From a graph of f'(x), how to find on what intervals f(x) is increasing or decreasing, f'(x) is increasing or decreasing, on what intervals f(x) is concave up or down, f'(x) is concave up or down?

Answer 1

This is the graph of f'(x)

Answer 2

Wherever the derivative, f'(x), is greater than 0 (so where the graph is above the x-axis), the function f(x) is increasing. Wherever f'(x) < 0 (so where it is below the x-axis), f(x) is decreasing.

I found a link with some more info and some diagrams. Concave up looks like a cup, concave down looks like a frown.
http://teachingcalculus.wordpress.com/2012/10/26/reading-the-derivatives-graph/