(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If an even degree polynomial of order 2n intersects the x-axis twice, how do I show that the (2n-1) th derivative has a zero in that interval?

2. Relevant equations

example: let g(x)=x^3(1-x). Show without computation that g'''(c) =0 for some c in (0, 1).

3. The attempt at a solution

I know that g' has a zero at x=1/2 because that is a maximum. I don't know how I can be sure that the 2nd and 3rd derivative have a zero in this interval.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# How do I show that a derivative of a polynomial has a zero in an interval?

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