A function $\mathrm{f}$ is defined by $\mathrm{f}\left( x \right)=a{{x}^{3}}+b{{x}^{2}}+cx+d$. T

Question

A function $\mathrm{f}$ is defined by $\mathrm{f}\left( x \right)=a{{x}^{3}}+b{{x}^{2}}+cx+d$. The graph of $y=\mathrm{f}\left( x \right)$ passes through the points $\left( 1,5 \right)$ and $\left( -1,-3 \right)$. The graph has a turning point at $x=1$, and $\displaystyle\int_{0}^{1}{\mathrm{f}\left( x \right)}\mathrm{d}x=6$. Find the values of $a$, $b$, $c$ and $d$.[5]

Accepted Answer

$a = 4, b = -6, c = 0, d = 7$

N2021 P1 Q1

N2021 P1 Q1

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