Math 129 Name______________________________________

Test 3

SHOW ALL RELEVANT WORK!!

1. Let .

a. Is f continuous on ? (2 pts)

b. Find the maximum and minimum of f on . (4 pts)

2. a. State the Mean Value Theorem including the necessary conditions. (2 pts)

b. Find c that satisfies the MVT for the following function on the indicated interval. (2 pts)

; [4, 7]

3. Let .

a. Identify the critical numbers for f. (2 pts)

b. Find the intervals on which f is increasing and on which f is decreasing. (4 pts)

c. Identify all relative extrema for f. (4 pts)

4. Let .

a. Determine the intervals on which f is concave up and on which f is concave down. (4 pts)

b. Identify all inflection points on the graph of f. (2 pts)

5. Given , find the following.

a. and intercepts. (3 pts)

b. vertical and horizontal asymptotes. (3 pts)

6. Sketch the graph of a function that satisfies the following. (6 pts)

i) vertical asymptotes at , horizontal asymptote at

ii) on (-2, 2)

iii) on (-¥, -2) È (2, ¥)

iv) on (-¥, -2) È (-2, 0)

v) on (0, 2) È (2, ¥)

vi) intercepts at (0, 0) and (-3, 0)

7. A rancher wants to form 3 adjacent corrals (see picture) using 1200 feet of fence. What is the maximum area he can enclose? (6 pts)

8. Let .

a. Write the differential dy. (3 pts)

b. Use dy to approximate the value of f (-0.1). (3 pts)