Answer:
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)
