MATH 101 Exam 2, Fall 2010

AMERICAN UNIVERSITY OF BEIRUT Mathematics Department Math 101 – Quiz II Fall 2010 – 2011 Name:………………………………………………. ID:……………………………………. Please circle your section number: Instructor: Silvana Jaber Section 1 Section 2 Section 3 Section 4 F @ 9:00 F @ 10:00 F @ 11:00 F @ 12:00 Instructions: 1. Write your NAME and AUB ID number above. 2. Solve the problems on the white sheets at the appropriate place. 3. You may use the blank and the back pages of the white sheet to solve or complete the solution of a problem. Part I / 20 Part II 1 /18 2 /12 3 /12 4 /24 5 /14 6 /6 7 /12 Total /118 PART I: Fill in the blanks. (20%) 1. If for all in the domain of , then is said to have _________ _________ at . 2. Can a local maximum also be an absolute maximum for a function ? (Yes or No) _________ 3. If , then either a local maximum or a local minimum at the interior point . (True or False) _________ 4. If has a local minimum at the interior point , then . (True or False) _________ 5. If the second derivative is positive, the curve of concave _________ at that point. 6. Does the condition guarantee a point of inflection? (Yes or No) _________ 7. If for all in an interval , then _________. 8. Suppose and its first derivative are continuous over . If and have opposite signs, then according to the Intermediate Value Theorem there is at least one point satisfying and _________. 9. Suppose the function has the derivative . Then the critical points of are _________. 10. Is continuous on ? (Yes or No) _________. -3 2 PART II: 1. a) (6%)Find horizontal and vertical asymptotes for the curve . b) (6%)Find the value of that verify the Mean Value Theorem. , c) (6%)Find the second derivative of . 2. (12%) Consider the function i. Does exist? ii. Does exist? iii. Does ? iv. Is continuous at ? 3. a) (6%)Find an equation for the tangent to the curve at the point . b) (6%)Find the absolute maximum and minimum values (if they exist) of over the interval . 4. (24%)Find the derivative of the following: a) b) c) d) e) f) 5. Let . a) (8%)Find the intervals in which the function is increasing and decreasing. b) (6%)Find the intervals in which the graph of concave up or concave down. 6. (6%)Find the tangent to the curve at the point (1, 0) 7. (12%)Let be the function with domain be given by Calculate: i. ii. iii. Find the values of and which make continuous at . BLANK PAGE