Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that f(a) = f(b). (Select all that apply.)

Question

f(x) = cot x

2

,

[𝜋, 3𝜋]

f(a) does not equal f(b) for all possible values of a and b in the interval [𝜋, 3𝜋].None of these.f '(a) does not equal f '(b) for any values in the interval [𝜋, 3𝜋].There are points on the interval (a, b) where f is not differentiable.There are points on the interval [a, b] where f is not continuous.

Answer 1

f(x) = cotx = cosx / sinx

sinx = 0 at x = π, 2π, 3π

So, f(x) is not defined at those points.

Therefore, f(x) is not continuous on the interval [π, 3π], so Rolle's Theorem is not applicable.