I gave the following question on a recent test. I believe I took it from a released AP MC test but I can't remember which or find it back. I remember the answer being C, but I was unable to come up with a counter example for III when my students asked. It doesn't seem like III has to be true, but I can't think of a situation where I and II are, but III isn't.
Let f be a fucntion such that lim (h->0) (f(2+h)-f(2))/h = 5. Which of the following MUST be true. I. f is continuous at x=2 II. f is differentiable at x=2 III. the derivative of f is continuous at x=2
a. I only b. II only c. I and II d. I and III e. II and III
Thanks, Kristin Visser
-- Mrs. Kristin Visser Chicago Christian High School Physics, Honors Physics, and AP Calculus Teacher Cross Country and Track Coach