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Sketch derivative branches around two vertical asymptotes

The diagram shows a sketch of y=f(x)y=f(x). (a) State the range of x for which f is strictly decreasing. (b) Sketch y=f′(x)y=f^{\prime}(x) on a separate diagram for all x.

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Given qualitative function with vertical asymptotes x=−2 and x=2: the negative outer-left branch falls to negative infinity; the central branch rises through the origin with a horizontal tangent; the positive outer-right branch falls towards 0.
Given qualitative function with vertical asymptotes x=−2 and x=2: the negative outer-left branch falls to negative infinity; the central branch rises through the origin with a horizontal tangent; the positive outer-right branch falls towards 0.
Given qualitative function with vertical asymptotes x=−2 and x=2: the negative outer-left branch falls to negative infinity; the central branch rises through the origin with a horizontal tangent; the positive outer-right branch falls towards 0.

[2006/IJC/Promo/7]

CJC · Lecture · Example 6

Mark where the original tangent is horizontal, then use its slope signs and the stated domain.

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