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