Let f be a function with selected values given in the table above. Which of the following statements must be true? I. By the Intermediate Value Theorem, there is a value c in the interval (0,3) such that f(c)=10.
II. By the Mean Value Theorem, there is a value c in the interval (0,3) such that f′(c)=−2. III. By the Extreme Value Theorem, there is a value c in the interval [0,3] such that f(c)≤f(x) for all x in the interval [0,3] .