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

Question

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 $d$.[4]

Accepted Answer

$a=3,\ b=0,\ c=-9,\ d=4$.

2025 SAJC P1 Q1

2025 SAJC P1 Q1

Solution:

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