Note that in order for this theorem to work then the

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Unformatted text preview: ) and notice that this is also an x-intercept. The coefficient of the 4th degree term is positive and so since the degree is even we know that the polynomial will increase without bound at both ends of the graph. Finally, here are some function evaluations. P ( -3) = 54 P ( -1) = -4 P (1) = -6 P ( 4 ) = 96 Now, starting at the left end we know that as we make x more and more negative the function must increase without bound. That means that as we move to the right the graph will actually be decreasing. At x = -3 the graph will be decreasing and will continue to decrease when we hit the first xintercept at x = -2 since we know that this x-intercept will cross the x-axis. Next, since the next x-intercept is at x = 0 we will have to have a turning point somewhere so that the graph can increase back up to this x-intercept. Again, we won’t worry about where this turning point actually is. Once we hit the x-intercept at x = 0 we know that we’ve got to have a turning point since this xintercept doesn’t cross the x-axis. Therefore to the right of x = 0 the graph will now be decreasing. It will continue to decrease until it hits a...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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