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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 . Page 2