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madelyn97

  • 2 years ago

The function f(x)=x^3-5x^2-2x=24 is positive for what parts of its domain?

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  1. Freyes
    • 2 years ago
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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

  2. Freyes
    • 2 years ago
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    can you factor it?

  3. madelyn97
    • 2 years ago
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    yep! thanks!

  4. satellite73
    • 2 years ago
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    is it \[ f(x)=x^3-5x^2-2x+24\]

  5. madelyn97
    • 2 years ago
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    yeah!

  6. satellite73
    • 2 years ago
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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

  7. satellite73
    • 2 years ago
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    |dw:1353208613053:dw|

  8. madelyn97
    • 2 years ago
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    |dw:1353208683477:dw|

  9. madelyn97
    • 2 years ago
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    but that doesnt work right?

  10. Freyes
    • 2 years ago
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    hmm i can factor this one out give me a second

  11. Freyes
    • 2 years ago
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    I think what you meant to do was \[(x+2)(x-3)(x-4)\]

  12. Freyes
    • 2 years ago
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    This gives you the ranges of \[(-\infty, -2) : (-2,3) : (3,4) :( 4,\infty)\]

  13. Freyes
    • 2 years ago
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    Then you can just plug a number from each of those ranges in between and just look at the sign.

  14. Freyes
    • 2 years ago
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    That'll tell you if it's in the positive range or not

  15. cinar
    • 2 years ago
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    |dw:1353216271826:dw|

  16. madelyn97
    • 2 years ago
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    okay thanks!

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