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Consider the function \(f\) whose second derivative is \(f^{\prime\prime}(x) = 3x -1\).

The graph of \(f\) has a minimum point at \(A(2 ; 4)\) and a maximum point at \(B(-\frac{4}{3}; \frac{358}{27})\).

1. Use the second derivative to justify that \(B\) is a maximum.
2. Given that \(f^\prime(x) = \frac{3}{2}x^2 - x + p\), show that \(p = -4\).
3. Find \(f(x)\).