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.
(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