Q21,Q23&Q33 needed to be solved correctly in 1 hour in the order to get positive feedbackThese are easy questions so solve these please do.all correctly 10.11.12.y=xMA13. Describe the way the slope changes as you move along thegraph (from left to right) in Exercise 5.14. Describe the way the slope changes on the graph in Exercise 6.15. Describe the way the slope changes on the graph in Exercise 8.16. Describe the way the slope changes on the graph in Exercise 10.Exercises 17 and 18 refer to the graph in Fig. 20.YABс.Fy = f(x)Figure 2017. (a) At which labeled points is the function increasing?(b) At which labeled points is the graph concave up?(c) Which labeled point has the most positive slope?18. (a) At which labeled points is the function decreasing?(b) At which labeled points is the graph concave down?2.1 Describing Graphs of Functions 139(c) Which labeled point has the most negative slope (that is,negative and with the greatest magnitude)?In Exercises 19-22, draw the graph of a function y=f(x) with thestated properties.19. Both the function and the slope increase as x increases.20. The function increases and the slope decreases as x increases.21. The function decreases and the slope increases as x increases.[Note: The slope is negative but becomes less negative.]22. Both the function and the slope decrease as x increases. [Note:The slope is negative and becomes more negative.]23. Annual World Consumption of Oil The annual world consump-tion of oil rises each year. Furthermore, the amount of the annualincrease in oil consumption is also rising each year. Sketch agraph that could represent the annual world consumption of oil.24. Average Annual Income In certain professions, the averageannual income has been rising at an increasing rate. Let f(T)denote the average annual income at year T for persons in one ofthese professions and sketch a graph that could represent f(T).25. A Patient's Temperature At noon, a child's temperature is101°F and is rising at an increasing rate. At 1 P.M. the child isgiven medicine. After 2 P.M. the temperature is still increasingbut at a decreasing rate. The temperature reaches a peak of 103°at 3 P.M. and decreases to 100° by 5 P.M. Draw a possible graphof the function 7(1), the child's temperature at time t.26. A Cost Function Let C(x) denote the total cost of manufactur-ing x units of some product. Then C(x) is an increasing func-tion for all x. For small values of x, the rate of increase of C(x)decreases (because of the savings that are possible with "massproduction"). Eventually, however, for large values of x, thecost C(x) increases at an increasing rate. (This happens whenproduction facilities are strained and become less efficient.)Sketch a graph that could represent C(x).27. Blood Flow through the Brain One method of determining thelevel of blood flow through the brain requires the person toinhale air containing a fixed concentration of N₂O, nitrousoxide. During the first minute, the concentration of N₂O inthe jugular vein grows at an increasing rate to a level of .25%.Thereafter, it grows at a decreasing rate and reaches a concen-tration of about 4% after 10 minutes. Draw a possible graphof the concentration of N₂O in the vein as a function of time.28. Pollution Suppose that some organic waste products aredumped into a lake at time r = 0 and that the oxygen contentof the lake at time t is given by the graph in Fig. 21. Describethe graph in physical terms. Indicate the significance of theinflection point at t = b.Oxygen content of waterteatbTime (days)Figure 21 A lake's recovery from pollution. 140 CHAPTER 2 Applications of the Derivative29. Number of U.S. Farms Figure 22 gives the number of U.S.farms in millions from 1920 (r= 20) to 2000 (t = 100). Inwhat year was the number of farms decreasing most rapidly?YU.S. Farms (millions)0 10(1900)Consumer price index(dollars)175160Time (years)og Figure 22 Number of U.S. farms.30. Consumer Price Index Figure 23 shows the graph of the con-sumer price index for the years 1983 (r= 0) through 2002( 19). This index measures how much a basket of com-modities that costs $100 in the beginning of 1983 would costat any given time. In what year was the rate of increase of theindex greatest? The least?190%14513011510020 30Tod30 40 50 60 70 80 90 100(2000)4070811O To0et (1983)basse gins Time (years)Figure 23 Consumer price index.31. Velocity of a Parachutist Let s(t) be the distance (in feet) trav-eled by a parachutist after t seconds from the time of openingthe chute, and suppose that s() has the line y = -15t + 10pibalSolutions to Check Your Understanding 2.11216t19(2002)1. The curve is concave up, so the slope increases. Even thoughthe curve itself is decreasing, the slope becomes less negativeas we move from left to right.2. At x = 3. We have drawn in tangent lines at three points inFig. 24. Note that as we move from left to right, the slopesdecrease steadily until the point (3, 2), at which time they startto increase. This is consistent with the fact that the graph isconcave down (hence slopes are decreasing) to the left of (3, 2)and concave up (hence, slopes are increasing) to the right of(3, 2). Extreme values of slopes always occur at inflectionpoints.as an asymptote. What does this imply about the velocity ofthe parachutist? [Note: Distance traveled downward is given anegative value.]32. Let P(1) be the population of a bacteria culture after / days andsuppose that P() has the line y = 25,000,000 as an asymptote.What does this imply about the size of the population?In Exercises 33-36, sketch the graph of a function having the givenproperties.33. Defined for 0≤x≤ 10; relative maximum point at x = 3;absolute maximum value at x = 1034. Relative maximum points at x = 1 and x = 5; relative mini-mum point at x = 3; inflection points at x = 2 and x = 435. Defined and increasing for all x ≥ 0; inflection point at x = 5;asymptotic to the line y = (2)x+ 536. Defined for x ≥ 0; absolute minimum value at x = 0; relativemaximum point at x = 4; asymptotic to the line y = () +137. Consider a smooth curve with no undefined points.(a) If it has two relative maximum points, must it have a rela-tive minimum point?(b) If it has two relative extreme points, must it have an inflec-tion point?38. If the function f(x) has a relative minimum at x = a and arelative maximum at x = b, must f(a) be less than f(b)?TECHNOLOGY EXERCISES39. Graph the function.f(x) =1x³2x²+x-2in the window [0, 4] by [-15, 15]. For what value of x doesf(x) have a vertical asymptote?40. The graph of the functionf(x) =2x²-15x+6has a horizontal asymptote of the form y= c. Estimate thevalue of e by graphing f(x) in the window [0, 50] by [-1, 6].41. Simultaneously graph the functionsFigure 241y=+x and y=xXin the window [-6, 6] by [-6, 6]. Describe the asymptote ofthe first function.(1, 1)(3, 2)(5, 4)A

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The function decreases and the slope increases as x increases. decreases as x increases. [Note: The slope is negative but becomes less negative.] 22. Both the function and the slope decrease as x increases. [Note: The slope is negative and becomes more negative.] 23. Annual World Consumption of Oil The annual world consump- tion of oil rises each year. Furthermore, the amount of the annual increase in oil consumption is also rising each year. Sketch a graph that could represent the annual world conm