How do you verify whether rolle's theorem can be applied to the function #f(x)=tanx# in [0,pi]?
The stickler for precision in me always wants to say, "Yes. For any function at all, Rolle's Theorem say: If
When we are asked whether some theorem "can be applied" to some situation, we are really being asked "Are the hypotheses of the theorem true for this situation?"
(The hypotheses are also called the antecedent, of 'the if parts'.)
So we need to determine whether the hypotheses ot Rolle's Theorem are true for the function
Rolle's Theorem has three hypotheses:
We say that we can apply Rolle's Theorem if all 3 hypotheses are true.
H1 : The function
At this point we could stop. Not all of the hypotheses are true. Let's look at the others for completeness.
H2 : The function
If even one hypothesis fails to be true, then we cannot apply the theorem.
Therefore we CANNOT apply Rolle's Theorem to