For each given function f and interval, determine if Rolle's Theorem guarantees the existence of some c in that interval with f'(c) = 0. If not, explain why not.
f(x) = \frac{1}{x + 1} on the interval (-1,1).
Answer
No. f(x) is not continuous on [-1,1] because f(-1) is undefined. We can't use Rolle's Theorem.