Question

can you apply Rolle's Theorem to the function f(x)=(cos)(pi)(x) on the closed interval [-1/6,1/6]?

Answer 1

Yes, you can.
i.) f(x) is continuous and differentiable on [-1/6, 1/6]
ii.) f(-1/6) = f(1/6)

Answer 2

Therefore there exists some point c such that -1/6 < c < 1/6 and
f'(x) = 0

Answer 3

oops, sorry, and f'(c) = 0

Answer 4

Thanks!