Monday, November 27, 2006

4-6 Graphing with Calculus and Calculators

Alright, this section is very similar to the previous section in that it deals with the graphs of functions and how calculus allows you to explore those functions. However, this section also talks about the presentation of a graph. Your calculator does not always give you the ideal window, for example. You can use calculus to make sure that you have included all the important parts of your graph in your final window.

Now for a sample problem!
Graph 3x^2-x+2 in a window that includes all important parts of the function.

Our first step is to find out all we can about the function using its first and second derivatives, following the procedure that Jean outlined so neatly in her post.

Increasing on: (0,inf)
Decreasing on: (-inf,0)
Local Maximum: none
Local Minimum: (.167,1.92)
Concave Up: (-inf,inf)
Concave Down: nowhere
Inflection Point(s): (.167,1.92)

You can see that the rather simple graph can be contained in a relatively small window. The ideal window would be something like x=[-2,2] and y=[+0 or -0 or 0,10]. Sorry about that; you got a compliment earlier. Here is the final graph:

Isabella, you are next in line for the joy that is blogging!

For those of you that are wondering, here are the next twenty digits:
pi=...62643383279502884197...

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