Selected values of a continuous function f are given below. Which of the following statements could be false?

Question

x 0 1 2 3 4

f(x) 2 -2 4 7 18

A. By the Intermediate Value Theorem applied to f on the interval [0, 4], there is a value c such that f(c) = 5.

B. By the Mean Value Theorem applied to f on the interval [0, 4], there is a value c such that f'(c) = 4.

C.By the Extreme Value Theorem applied to f on the interval [0, 4], there is a value c such that f(c)≤ f(x) for all x in [0,4].

D. By the Extreme Value Theorem applied to f on the interval [0, 4], there is a value c such that f(c)≥ f(x) for all x in [0,4].

Answer 1

As it is continuous on [0, 4] and f(0) = 2 < 5 < f(4) = 18, it meets the conditions for a, c, and d.

It is not given that it is continuously differentiable, so it does not meet the conditions for b.