Math 229 Lab 17: Section 14.1 Name: Use good notation and show all of your work. 1. The number of bank burglaries (entry into or theft from a bank during non-business hours) in the united states for the years 2000-2009 is given in the figure below. Consider the closed interval [2000, 2009]. Bank Burglaries (2000-2009) (a) Give all relative maxima and minimum and when the 450 occur on the interval. Interpret your results. 400 350 341 300 304 250 254 209 218 200 150 -134 121 131- 158 100 50 100 0 (b) Give the absolute maxima and minima and when th 2000 2002 2004 2006 2008 occur on the interval. Interpret your results. Year 2. A company had found that its weekly profit from the sale of a car transmissions is given by P(x) = -0.02x3 + 600x - 20000. Production bottlenecks limit the number of transmissions that can be made per week to no more than 150, while a long-term contract requires that at least 50 transmissions be made each week. Find the maximum possible weekly profit that the firm can make. Page 1Math 229 Lab 17: Section 14.1 Name: 3. Find the absolute extrema of the function f(x) = x8/3 - 16x2/3 on the interval [-1, 8]. f ( x) = 8 / x 32 0 = 8/3x /3 - 32 x 4. A charter bus company charges a fare of $40 per person, plus $2 per person for each unsold seat on the bus. The bus holds 100 passengers and let u represents the number of unsold seats. (a) What is the implied domain? (b) Give the revenue function. (c) How many passengers must ride to produce the maximum revenue? What is the maximum revenue? Page 2