Question 2. ?
Math 1100 Midterm 2 April 1 First and Last Name: UnID: Instructions: You have time till 11:59 pm tomorrow (April 2) to complete the exam. Show all your work. Partial credit may be given for work, and solutions with no work shown may not receive full credit. Only writing the final answer with no clear steps or explanation will not earn you any points. You can use any resource available to you including the internet in order to answer these questions. The number next to a question is how many points the question is worth. 1 15 1. Suppose the weekly demand function for a product is q= 5000 1 1 + e2p where p is the price in thousands of dollars and q is the number of units demanded. What is the elasticity of demand when the price is $1000 and the quantity demanded is 595. Page 2 of 8 25 2. For the function y= x+2 3 =1+ x1 x1 answer the following questions. (a) (5 points) Find the horizontal and vertical asymptotes, if they exist. If no asymptote exists, state that clearly. Explain how you reached your answer. VA HA (b) (8 points) Find the derivative function f 0 (x) and draw the sign line for f 0 (x). f 0 (x) = - Page 3 of 8 (c) (5 points) Find all the min/max point(s) if they exist. If they do not exist, state that clearly. Minima Maxima What it means (d) (7 points) Find all the inflection point(s) if they exist. If they do not exist, state that clearly. Inflection point(s) - Page 4 of 8 20 3. For the implicitly given curve 6 + ex y = y 2 + 3x. Find the equation of the tangent line to the curve at the point (2, 0). Equation of tangent line - Page 5 of 8 15 4. For a product, the profit function is given by P (x) = x2 + 81x 80 40 ln x, where x is the number of items sold. (a) (15 points) How many items should be sold to earn maximum profit? Number of items = (b) (5 points) What is the maximum profit? Max profit = Page 6 of 8 25 5. A young woman needs to rescue her friend from a cruel witch, who has the friend locked up in a room, way up high. The woman has placed a 25 foot ladder against the witch's house and climbed to the top of the ladder to knock on the window of her friend. The witch starts pulling the bottom of the ladder away from the house which makes the top of the ladder (and the young woman) fall vertically at the rate of 4 feet per second. How fast is the witch pulling the ladder away from the bottom of the wall, when the bottom of the ladder is 15 feet away from the bottom of the wall. NOTE - To earn full points, draw the figure and provide all the details. ANSWER - Page 7 of 8 Question Points 1 15 2 25 3 20 4 15 5 25 Total: 100 FINAL SCORE (out of 100) = Page 8 of 8 Score
