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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 isnt 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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This note was uploaded on 01/07/2010 for the course MAT mat1300 taught by Professor Pieterhofstra during the Fall '09 term at University of Ottawa.
 Fall '09
 PIETERHOFSTRA

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