Mathematics

Consider the function \(f\) with the second derivative \(f''(x) = 3x - 1\). The graph of \(f\) has a minimum point at \(\mathrm{A}(2,4)\) and a maximum point at \(\mathrm{B} \left( - \frac{4}{3}, \frac{358}{27} \right)\).

1. Use the second derivative to justify that \(\mathrm{B}\) is a maximum.[3]
2. Given that \(f' = \frac{3}{2}x^2 - x + p\), show that \(p = -4\).[4]
3. Find \(f(x)\).[7]