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- anonymous

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

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- anonymous

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

- jamiebookeater

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- 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

- anonymous

can you factor it?

- anonymous

yep! thanks!

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- anonymous

is it \[ f(x)=x^3-5x^2-2x+24\]

- anonymous

yeah!

- 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

- anonymous

|dw:1353208613053:dw|

- anonymous

|dw:1353208683477:dw|

- anonymous

but that doesnt work right?

- anonymous

hmm i can factor this one out give me a second

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

|dw:1353216271826:dw|

- anonymous

okay thanks!

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