Math 1210
Extra credit for Midterm 2
February 28th, 2014
Answer the following two (2) questions. The value of every question is
indicated at the beginning of it. This will count towards extra credit in your
second midterm score. I WILL ONLY COLLECT THIS ON TUESDAY: you
can either bring it to class or to my office.
Name:
UID:
1. (9 points) In Figure 1 below you can see the graph of the DERIVATIVE f 0 of a function
f . Assume that f (−3) = 2, f (−2) = 0, f (−1) = −2, f (0) = 5 and f (2) = 0.
Figure 1: Question 2
(i) (3 points) Over which intervals is f increasing/decreasing? What are (if any) its
local extreme values?
(ii) (3 points) Over which intervals is f concave up/down? What are (if any) the
inflection points of f ?
(iii) (3 points) Sketch the graph of f .
2. (20 points) Consider the function f (x) =
(x−1)(x−3)
(x+1)(x−2)
over (−∞, +∞).
1. (2 points) What is the domain of f ? Describe the discontinuities at the x-values
for which f is not defined.
2. (2 point) Compute the limits limx→+∞ f (x) and limx→−∞ f (x).
3. (4 points) Over which intervals is f increasing (resp. decreasing)? Namely, for
which x is f 0 (x) positive (resp. negative)?
4. (2 points) What are, if any, the local extreme values of f ?
5. (4 points) Over which intervals is f concave up (resp. down)? Namely, for which x
is f 00 (x) positive (resp. negative)?
6. (2 points) What are, if any, the inflection points of f ?
7. (4 points) Sketch the graph of f .
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