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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.

Solve the inequalities f'(x) > 0 and f'(x) < 0 using symbolic notation and intervals.

Learn how to solve inequalities involving the derivative of a function, focusing on the intervals where f'(x) > 0 and f'(x) < 0. This problem covers key calculus concepts, including the first derivative test and critical points analysis. Suitable for college-level calculus students.

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