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Let \(f(x) = ax^3 + bx^2 + c\), where \(a\), \(b\) and \(c\) are real numbers. The curve of \(f\) passes through the point \(( 2; 9 )\).

1. Show that \(8a + 4b +c = 9\).

The curve of \(f\) has a local minimum at \((1; 4)\).

2. Find two more equations in terms of \(a\), \(b\) and \(c\), giving your answers in a form similar to that of part A.
3. Find the value of \(a\), the value of \(b\) and the value of \(c\).