Final answer:
To verify Lagrange's Mean Value Theorem for the function f(x) = x - 2sinx on the interval [−π, π], we confirmed that f(x) is both continuous on the closed interval and differentiable on the open interval, allowing us to proceed with the theorem's application.
Step-by-step explanation:
To verify Lagrange's Mean Value Theorem for the function f(x) = x - 2sinx on the interval [−π, π], we need to first ensure that the function is continuous on the closed interval [−π, π] and differentiable on the open interval (−π, π). The function f(x) = x - 2sinx is a combination of a polynomial function and a trigonometric function, both of which are continuous and differentiable everywhere. Therefore, f(x) is continuous on [−π, π] and differentiable on (−π, π), satisfying the conditions for applying Lagrange's Mean Value Theorem.