P is a polynomial of degree 6. M and N are two real numbers with 0 < M < N. Given that:

1. P(M) = P(-M), and:
2. P(N) = P(-N)
3. P’(0) = 0

Does the relationship P(x) = P(-x) hold for all nonzero real values of x?
If so, prove it.
If not, provide a counterexample.

(In reply to Counterexample by Ady TZIDON)

I interpreted the third condition to be referring to the first derivative of P(x).  If that interpretation is correct, then the proposed counterexample fails.

Edited on May 13, 2015, 9:37 pm

Posted by Steve Herman on 2015-05-13 08:47:47