Porisma

A hint to get started

Transfer an oblique asymptote to the derivative sketch

The diagram shows the graph of y=f(x)y=f(x). Sketch the curve of y=f′(x)y=f^{\prime}(x).

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Given function with asymptotes x=3 and y=−x+2, y-intercept 7/3, minimum (2,1) on the left branch and maximum (4,−3) on the right. The left branch tends up without bound at 3 from the left; the right starts at negative infinity and rises to its maximum before falling.
Given function with asymptotes x=3 and y=−x+2, y-intercept 7/3, minimum (2,1) on the left branch and maximum (4,−3) on the right. The left branch tends up without bound at 3 from the left; the right starts at negative infinity and rises to its maximum before falling.
Given function with asymptotes x=3 and y=−x+2, y-intercept 7/3, minimum (2,1) on the left branch and maximum (4,−3) on the right. The left branch tends up without bound at 3 from the left; the right starts at negative infinity and rises to its maximum before falling.

[2010/VJC/Promo/6(ii)]

CJC · Lecture · Example 7

Read horizontal tangents at 2 and 4, then inspect slope signs on each side of 3.

Read the worked solution