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Unformatted text preview: Lecture 12  Curve Sketching 12.1 Curve Sketching This section is a summary of the information we have gained in this chapter and how to apply it to sketching the graph of a given function. When asked to graph a function, your graph should take into account the following information: • xintercepts and yintercept, • domain, • continuity (ie places where it is not continuous), • differentiability (ie places where it isn’t differentiable), • local maxes and mins, • intervals of increase and decrease, • intervals of concavity, • points of inflection, • asymptotes. Examples: 1. Sketch the graph of y = f ( x ) = x 3 + 3 x 2 9 x 11. solution: We try to find all the information in the list above • To find the yintercept we find f (0) = 11. So the yintercept is (0 , 11). The xintercepts in this example are a bit tricky to find (and you are not expected to do this from scratch). More often I will give you one of the roots and you will have to find the other one. Here, one of the roots is x = 1. Thus ( x + 1) has to be a factor of f ( x ), and you can find by long division (or any other method) that...
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 Fall '09
 PIETERHOFSTRA
 Real Numbers, Derivative, Mathematical analysis, local max

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