Provide an appropriate response.The function f(x) = is zero at x = 0 and x = 1 and differentiable on (0, 1), but its derivative on (0,1) is never zero. Does this example contradict Rolle's Theorem?

Question

What will be an ideal response?

Answer 1

This example does not contradict Rolle's Theorem because the function f is not continuous on the closed interval [0, 1]. In particular, f is not continuous at the right end point x = 1.