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Sketch a derivative across two vertical asymptotes

The diagram, not to scale, shows the graph of y=f(x)y=f(x). The vertical asymptotes are x=0x=0 and x=2x=2. Sketch the graph of y=f′(x)y=f^{\prime}(x), showing all corresponding coordinates and asymptotes where possible. marks

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Qualitative graph, not to scale: local maximum A(-1,2) on the negative-x branch, zero at -0.5, vertical asymptote x=0; between 0 and 2 a U-shaped branch has minimum B(1,3); beyond x=2 the curve rises from negative infinity towards the x-axis. No numerical function is supplied.
Qualitative graph, not to scale: local maximum A(-1,2) on the negative-x branch, zero at -0.5, vertical asymptote x=0; between 0 and 2 a U-shaped branch has minimum B(1,3); beyond x=2 the curve rises from negative infinity towards the x-axis. No numerical function is supplied.
Qualitative graph, not to scale: local maximum A(-1,2) on the negative-x branch, zero at -0.5, vertical asymptote x=0; between 0 and 2 a U-shaped branch has minimum B(1,3); beyond x=2 the curve rises from negative infinity towards the x-axis. No numerical function is supplied.

[2010/SRJC/I/6(a)]

CJC · Review problems · Question 1

Convert increasing/decreasing intervals to positive/negative derivative values.

Read the worked solution