Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.)

Question

f(x) = 2 cos 𝜋x,    [0, 2]

If Rolle's theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = 0.

 (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)

c =

Answer 1

At the end points of interval [0, 2] f(0) = 2cos0 = 2 = 2cos2π = f(2).

f(x) continuis on [0, 2] and differentiable on (0, 2).

So by Rolle's Theorem f'(c) = - 2πsinπc = 0; sinπc = 0; πc = π; c = 1