Suppose p is a polynomial with real coefficients. Then which of the following statements is necessarily true?
1
There is no root of the derivative p' between two real roots of the polynomial p .
2
There is exactly one root of the derivative p' between any two real roots of p .
3
There is exactly one root of the derivative p' between any two consecutive roots of p .
4
There is at least one root of the derivative p' between any two consecutive roots of p .