A function \(\mathrm{f}\) is defined by \(\mathrm{f}(x) = ax^3 + bx^2 + cx + d\) where \(a\), \(b\), \(c\) and \(d\) are constants.
The graph of \(y = \mathrm{f}(x)\) has a turning point at \(x = -1\) and passes through the points \((2, 10)\) and \((-2, -2)\).
Given also that \(\int_{-2}^{2} \mathrm{f}(x) \, \mathrm{d}x = 16\) find the values of \(a\), \(b\), \(c\) and \(d\).[4]

A function \(\mathrm{f}\) is defined by \(\mathrm{f}(x) = ax^3 + bx^2 + cx + d\) where \(a\), \(b\), \(c\) and \(d\) are constants.

The graph of \(y = \mathrm{f}(x)\) has a turning point at \(x = -1\) and passes through the points \((2, 10)\) and \((-2, -2)\).

Given also that \(\displaystyle \int_{-2}^{2} \mathrm{f}(x) \, \mathrm{d}x = 16\) find the values of \(a\), \(b\), \(c\) and \(d\).

2025 SAJC P1 Q1

2025 SAJC P1 Q1