1. ## Rolles Theorem

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?

2. What about $c=0?$

3. you mean f'(c)=0?

b/c c=0 = 1 which is outside the intervals as well... right?

4. Originally Posted by action812
you mean f'(c)=0?
b/c c=0 = 1 which is outside the intervals as well... right?
That is nonsense. $\frac{-1}{6}<0<\frac{1}{6}$.

5. so the derivative set to zero = zero.

therefore the asnwer is x= 0 for the whole problem? correct?