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.

apparently we have solved correctly different problems:

SH:

- P(M) = P(-M), and:
- P(N) = P(-N)
- P’(0) = 0

AT

- P(M) = P(-M), and:
- P(N) = P(-N)
- P(0) = 0

**SH solved the posted puzzle, AT - what he saw...**

Vive la petite difference!