A cubic polynomial $y = ax^{3}+bx^{2}+cx+d$ satisfies the following conditions: $y(0)=2$, $y(1)=5$, the curve has a turning point at $x=2$ (so $y'(2)=0$), and it passes through the origin of the x‑axis at $x=2$ (so $y(2)=0$).

(i) Determine the coefficient $a$.

(ii) Find the exact area enclosed between the curve and the x‑axis from $x=0$ to $x=2$.

Question

A cubic polynomial $y = ax^{3}+bx^{2}+cx+d$ satisfies the following conditions: $y(0)=2$, $y(1)=5$, the curve has a turning point at $x=2$ (so $y'(2)=0$), and it passes through the origin of the x‑axis at $x=2$ (so $y(2)=0$).
 
(i) Determine the coefficient $a$.
 
(ii) Find the exact area enclosed between the curve and the x‑axis from $x=0$ to $x=2$.

Accepted Answer

a = \frac{9}{2}; 	ext{Area} = \frac{22}{3}

Gce Model Questions Vol1 2021 Further Mathematics Question 19

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