The curve $C$ is given by the equation $y=\frac{1}{x}+\frac{2}{x^2}, x \neq 0$. Without using a

Question

The curve $C$ is given by the equation $y=\frac{1}{x}+\frac{2}{x^2}, x \neq 0$. Without using a calculator, find the set of values that $y$ can take.[2] Sketch the curve $C$, stating the equations of any asymptotes and the coordinates of any turning points and points of intersection with the axes.[3] Given that the solution of the inequality $ax^2+bx+c > \frac{1}{x}+\frac{2}{x^2}$ is the set $\{x \in \mathbb{R} : -1.5 < x < -1 \text{ or}\hspace{0.5em} 1 < x < k\}$, find the values of $a$, $b$ and $c$.[3] Hence find the value of $k$.[1]

Accepted Answer

(i) $\left\{ y\in \mathbb{R}:y\ge -\dfrac{1}{8} \right\}$ (ii) $x=0,\ y=0$; $a=-\dfrac{2}{9},\ b=1,\ c=\dfrac{20}{9}$, $k=6$

2015 ACJC P1 Q9

2015 ACJC P1 Q9

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