Without using a calculator, solve the inequality $\frac{4x}{{{x}^{2}}-3x-4}\ge -x$. Hence solve th

Question

Without using a calculator, solve the inequality $\frac{4x}{{{x}^{2}}-3x-4}\ge -x$. Hence solve the inequality $\frac{4\left| x \right|}{{{x}^{2}}-3\left| x \right|-4}<-\left| x \right|$.[6] The diagrams below show the graphs of $y=\left| \mathrm{f}(x) \right|$ and $y=\mathrm{f}'(x)$. Sketch the graph of $y=\mathrm{f}(x)$, labelling the equations of any asymptotes and the coordinates of the turning point and the points where the curve crosses the axes.[3]

Accepted Answer

(a) $-14$; hence $-4<x<-3$ or $3<x<4$ (b) Intercepts $(-1,0)$, $(2,0)$, $(0,3)$; maximum $(0,3)$; asymptotes $x=4$, $y=-2$ on the left, and $y=0$ on the right

2020 NJC Promo Q6

2020 NJC Promo Q6

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