As can be seen in the above graph:
(a) g(x) > 0 in the interval: (-4, -2) U (0, 2)
(b) g(x) < 0 in the interval: (-2, 0)
(c) g(x) = 0 at the next x-values: -4, -2, 0, 2
Graphically, the derivative of a function evaluated at a point is seen as the slope of the tangent line that passes through that point of the function.
Then, if the slope is positive, the derivative is positive, if the slope is zero (a horizontal line), the derivative is zero, and if the slope is negative, the derivative is negative.
In the next graph, we can see some of these slopes:
Therefore, the intervals where g'(x) is positive, negative or zero are:
(d) g'(x) > 0 in the interval: (-4, -3) U (-1, 1)
(e) g'(x) < 0 in the interval: (-3, -1) U (1, 2)
(f) g'(x) = 0 at the next x-values: -3, -1, 1