Statement : If the graph of a 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 function may be rational or polynomial function.

The statement satisfies the Rolles Theorem if and only if the function is polynomial function.

So the statement is false for the function which does not satisfies the                    Rolles Theorem.

Therefore the statement is false.

False.