Date: Dec 1, 2011 5:33 PM
Author: Kristin Visser
Subject: [ap-calculus] MC question

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

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