madelyn97
The function f(x)=x^3-5x^2-2x=24 is positive for what parts of its domain?
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Freyes
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Well in this situation the best thing to do would be to simplify it.. into factors. then you have ranges of test cases to test whether a number is positive in that range
Freyes
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can you factor it?
madelyn97
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yep! thanks!
anonymous
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is it \[ f(x)=x^3-5x^2-2x+24\]
madelyn97
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yeah!
anonymous
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did you factor? once you have the three zeros, because this is a third degree polynomial with positive leading coefficient you know it will be
negative, then positive, then negative, then positive
anonymous
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|dw:1353208613053:dw|
madelyn97
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|dw:1353208683477:dw|
madelyn97
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but that doesnt work right?
Freyes
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hmm i can factor this one out give me a second
Freyes
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I think what you meant to do was
\[(x+2)(x-3)(x-4)\]
Freyes
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This gives you the ranges of \[(-\infty, -2) : (-2,3) : (3,4) :( 4,\infty)\]
Freyes
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Then you can just plug a number from each of those ranges in between and just look at the sign.
Freyes
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That'll tell you if it's in the positive range or not
cinar
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madelyn97
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okay thanks!