The problem statement, all variables and given/known data a. If f is defined on an interval [x,y], its differentiable on open interval (x,y), and f(x)=f(y) then there is a number c in (x,y) where f'(c)=0 b. Does the absolute value of x, |x|, satisfy Rolle's Theorem on [-1, 1]? The attempt at a solution For the first one, I'm not really sure. But for the second, I believe it does not satisfy. Because when x =0 on the interval, it is not differentiable.