To solve these inequalities, we need information about the function $f'(x)$. The task asks for the intervals where $f'(x) > 0$ (where the derivative is positive, indicating that the function $f(x)$ is increasing) and $f'(x) < 0$ (where the derivative is negative, indicating that $f(x)$ is decreasing).

However, the problem hints that the solution should use information from where $f'(x) = 0$, which is likely from a previous part (part (a) as mentioned). To proceed, we need to:

1. Identify the critical points, which are the points where $f'(x) = 0$ or $f'(x)$ is undefined.
2. Analyze the behavior of $f'(x)$ around these critical points to determine where it is positive and negative.

Could you provide more details or information from part (a) or describe the function $f'(x)$? This will help me to determine the intervals properly.