Consider the following. (If an answer does not exist, enter DNE.) f ' (x) = x2 + x - 20 (a) Find the open intervals on which f ' (x) is increasing or decreasing.

f' (x) is increasing in the open interval (-1/2, + ∞), and it is decreasing in the interval (-∞, - 1/2).

Step-by-step explanation:

f' (x) is a quadratic function with positive main coefficient, then it will be decreasing until the x-coordinate of its vertex and it will be increasing from there onwards. The x-coordinate of the vertex is given by the equation - b/2a = - 1/2. Hence

- f' (x) is incresing in the interval (-1/2, + ∞)

- f' (x) is decreasing in the interval (-∞, - 1/2)