2015 JJC P1 Q8
2015 JJC P1 Q8
The diagram below shows the curve with equation \(y=\mathrm{f}\left( x \right)\) which has vertical asymptotes \(x=a\) and \(x=-a\) where \(a>0,\)horizontal asymptote \(y=0\) and a stationary point at \(\left( 0,-1 \right)\).
Sketch, on separate diagrams, the graphs of
- \(y=\frac{1}{\mathrm{f}\left( x \right)}\),
- \(y=\mathrm{f}'\left( x \right)\).
Solution:
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Answer:(a) Minimum \((0,-1)\); holes at \((-a,0),(a,0)\); negative between them, positive outside, unbounded upwards at both outer ends. (b) Zero \((0,0)\); positive for \(x<0\), negative for \(x>0\), excluding \(x=\pm a\); asymptotes \(x=\pm a\) and \(y=0\). See the worked sketches.
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