Question

Which of the following statements is/are true? (5 points)

Answer 1

Here are the statements:

I.If f '(x) exists and is nonzero for all x, then f(1) ≠ f(0) TRUE
II.If f is differentiable for all x and f (-1) = f(1), then there is a number c, such that |c| < 1 and f '(c) = 0. FALSE
III.If f '(c) = 0, then f has a local maximum or minimum at x = c. TRUE

So, the correct answer is I and III only.