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

1. anonymous

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. anonymous

can you factor it?

3. anonymous

yep! thanks!

4. anonymous

is it $f(x)=x^3-5x^2-2x+24$

5. anonymous

yeah!

6. anonymous

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. anonymous

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8. anonymous

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9. anonymous

but that doesnt work right?

10. anonymous

hmm i can factor this one out give me a second

11. anonymous

I think what you meant to do was $(x+2)(x-3)(x-4)$

12. anonymous

This gives you the ranges of $(-\infty, -2) : (-2,3) : (3,4) :( 4,\infty)$

13. anonymous

Then you can just plug a number from each of those ranges in between and just look at the sign.

14. anonymous

That'll tell you if it's in the positive range or not

15. anonymous

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16. anonymous

okay thanks!