Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 12. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | Reading a Graph to Get Information About a Function 91 from east to west. We use noon as our benchmark time noon corresponds to time t 0. Therefore time t 2 is 10 00 . position TRIP III position - 4 2 TRIP IV Answer parts a b and c for each of the trips corresponding to graphs I II III and IV. a For what values of t is velocity positive When is travel from west to east b For what values of t is velocity negative When is travel from east to west c To which trip do each of the following velocity graphs correspond Be sure your answer to part c agrees with your answers to parts a and b . velocity velocity 2 -1 A t -2 B velocity t -3 -2 1 2 C velocity When you have completed your work on this problem compare your answers with those of one of your classmates. If you disagree about an answer each of you should discuss your reasoning and see if you can come to a consensus on the answers. 5. Look back at the figures for Problem 4. What characteristic of the graph of position versus time determines the sign of the velocity 6. An ape with budding consciousness throws a bone straight up into the air from a height of 2 From the seven graphs that follow pick out the one that could be the bone s a height versus time b velocity versus time c speed versus time. 15 Problem by Eric Brussel. 92 CHAPTER 2 Characterizing Functions and Introducing Rates of Change 7. The velocity of an object is given in miles per hour by t 2t5 6t3 2t2 1 over the time interval 2 t 2 where t is measured in hours. Use your graphing calculator to answer the following questions. a Sketch a graph of the velocity function over the time interval 2 t 2. b Approximately when does the object change direction Please give answers that are off by no more than . Either use the zoom feature of your calculator or change the domain until you can answer this question. If your calculator has an equation solver use that as well and compare the answers you arrive at graphically with the answers you get .
