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lecture12 - Lecture 12 Curve Sketching 12.1 Curve Sketching...

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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: • x-intercepts and y-intercept, • 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 y-intercept we find f (0) =- 11. So the y-intercept is (0 ,- 11). The x-intercepts 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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lecture12 - Lecture 12 Curve Sketching 12.1 Curve Sketching...

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