The curve $C$ has the equation $y=ax+\frac{b}{x-2}$, where $a$ and $b$ are non-zero con

Question

The curve $C$ has the equation $y=ax+\frac{b}{x-2}$, where $a$ and $b$ are non-zero constants. State the condition(s) required for $a$ and $b$ for this curve to have two turning points.[2] Given that $a=b$, find the range of values of $y$ can take, in terms of $a$.[4] The inequality $ax+\frac{b}{x-2} < ax+m$ where $a>0$, $b<0$ and $m$ is a positive constant, has the solution set $\{x\in \mathbb{R}:x<0$ or $x>2\}$. Find $m$ in terms of $b$.[2]

Accepted Answer

(i) $a>0$, $b>0$ or $a0$, then $y\le 0$ or $y\ge 4a$. If $a<0$, then $y\le 4a$ or $y\ge 0$. (iii) $m=-\frac{b}{2}$

2020 DHS P1 Q4

2020 DHS P1 Q4

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