Calculus true/false question?

Question

If the graph of a polynomial function has four x-intercepts, then it must have at least three points at which its tangent line is horizontal.

True or false? Explain?

Answer 1

true, because if it has four x - intercepts, that means it has 3 points of inflection, points of inflection are where the tangent lines to the graph of the function change their slope from positive to negative or vice versa.

Answer 2

That would be true of any sufficiently well-behaved function (say, with a second derivative defined everywhere), not just polynomials.