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

Given that:

- P(M) = P(-M), and:
- P(N) = P(-N)
- 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**