Final answer:
Rolle's theorem cannot be applied to the given inequality 2x - 6y < 12.
Step-by-step explanation:
Rolle's theorem is a theorem in calculus that states that if a function is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and the function values at the endpoints are equal, then there exists at least one point c in (a, b) at which the derivative of the function is zero.
In this case, we have the inequality 2x - 6y < 12. This is not an equation, but an inequality. Rolle's theorem can only be applied to a function, not an inequality. Therefore, we cannot determine whether Rolle's theorem can be applied to f on the closed interval [a, b] based on the given inequality.