Part a
Given that the derivative of \(f(x)\) is \(f'(x)= 3ax^2 + 2bx + c\), determine the intervals on which \(f'(x)\) is positive or negative. Use your analysis to deduce where \(f(x)\) is increasing (\(f'(x)>0\)) and where it is decreasing (\(f'(x)<0\)).