- #1

- 863

- 4

I'm not in school anymore, just an interested engineer. Does anyone know where I can find this proof or any really

*strong*hints on how to do it myself? I've been out of it for a while and I'm rusty.

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- Thread starter KingNothing
- Start date

- #1

- 863

- 4

I'm not in school anymore, just an interested engineer. Does anyone know where I can find this proof or any really

- #2

Deveno

Science Advisor

- 906

- 6

you don't even need limits for this, you can just define a derivative formally using the power rule.

why derivatives? because, in general, all one can say at the outset, is that a polynomial of odd degree has at least one root. to bring the IVT to bear, one has to find out how many times a polynomial p(x) can "change direction", that is, when its slope changes sign.

for an partial example of how this becomes an induction proof:

suppose p(x) is of degree 2, so that p(x) = ax

this means that p(x) changes direction exactly once (for higher degrees it becomes "at most n-1 times" because some of the "humps" might not exist (f(x) = x

you should be able to generalize, and make this a bit more rigorous, from this little bit.

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