The function f(x) from the graph f'(x)

1. The function is increasing at (-2,0) and (0,2)
The function is decreasing at (-∞,-2) and (2,∞)
You can tell because at these intervals the outputs are the same as the slope of f(x). Increasing means the slope is positive and decreasing means the slope is negative.

2. There are possible extrema at the points x=-2, x=0, x=2 because at those points the output is zero.

3. At (-1,0) and (1,-∞) f(x) is concave down and at (-∞,1) and (0,1) f(x) is concave up because the slope of f'(x) is negative @ (-1,0) and (1,-∞) and positive @ (-∞,1) and (0,1).

4.The function is possibly either f(x)=sinx or f(x)=cosx.