Determine whether Rolles Theorem can be applied to f(x)=cos(pi*x) on the closed interval [ -1/6, 1/6]. If so, find all #'s c in the open interval (-1/6,1/6) such that f'(c) =0.

My results: I started by checking if it is continuous, which it is. Then if its differentiable, which it is. The end points ( -1/6, 1/6) also return the same value. So then I send the derivative to zero

which looked like 0= -pi*sin(pi*x)

which equals 2pi.. therefore Rolles Theorem doesnt not apply. Correct me if I'm wrong?