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

Rolles Theorem :

Let  be a function that satisfies the following three hypotheses.

1.  is continuous on .

2.  is differentiable on .

3. .

Then there is a number  in  such that .

The statement is true if and if the function satisfies the Rolles Theorem.

The polynomial function is continuous and differentiable in its domain.

So the polynomial function satisfies the Rolles Theorem.

Therefore the statement is true.

True.