- #1

Charles49

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## Homework Statement

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?

## Homework Equations

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

## 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.