lTopic: Inection points and critical points {Maxim} 0 An application of inection points and critical points to a diabetic student's blood sugar love}. (20%) Iessica's Blood Sugar Level Pictures taken Friday, November 16, 2012 Basics The monitor beepsfvibrates when there is a problem. The pump constantly adds insulin to her body. ' The ideal level is between 80 and 120. ' If the level drops too low, she eats sugar and protein. ' If the level is dropping too fast at any time, she eats sugar and proteii ' Ifthe level rises too high, she takes an insulin shot. ' Ifthe level is rising too fast at any time, she takes an insulin shot. l Times ' 5.5 hours ago: ate breakfast ' 5 hours ago: insulin shot - 2 hours ago: ate sugar and protein Elam}: ' Mark the times shown above on the pictures [the first shows 3 httlursr the second shows 6 hours] - Mark the min's and max's - these are the critical points. Questions Part 1: 1. Did eating 5.5 hours ago create a critical point or inection point? Why? 2. Did the monitor beep 5 hours ago because of the level or the rate? 3. Did taking the insulin shot create a critical point or inection point? Why? 4. Did eating the sugar and protein create a criticai point or inection point? Why? 5. Summarize the meaning of "inection point" for the sugar level example. 6. What does it mean in calculus to sayr the level is rising or dropping too fast? Questions Part 2: Use the following graph to estimate the following: 1. When was lunch eaten? 2. Was a shot taken? If so, then when was it taken