Q33 needed asapPlease solve correctly do via by Hand 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 (100). Inwhat year was the number of farms decreasing most rapidly?GU.S. Farms (millions)adtmodeYdera (1900)0 10 20 30 40 50 60 70 80 90 100(2000)Time (years)Figure 22 Number of U.S. farms.Consumer price index(dollars)30. Consumer Price Index Figure 23 shows the graph of the con-sumer price index for the years 1983 (r= 0) through 2002(119). 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?19017516014513011510001 cod sku20Oh to ho0et (1983)3300Tom802411216CEt19(2002)4bas stan ge 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(t) has the line y = -15t + 10sinibal levingle af de dSolutions to Check Your Understanding 2.11. 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 inflection.points.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()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 functionf(x) =in the window [0, 4] by [-15, 15]. For what value of x doesf(x) have a vertical asymptote?40. The graph of the function1x32x²+x-2f(x)=2x²-1.5.x² +6has a horizontal asymptote of the form y = c. Estimate theod value of c by graphing f(x) in the window [0, 50] by [-1, 6].41. Simultaneously graph the functions.Figure 241y=+x and y = xXin the window [-6, 6] by [-6, 6]. Describe the asymptote ofthe first function.Y(1, 1)(3, 2)(5, 4)dolce

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In Exercises 33-36, sketch the graph of a function having the given properties. 33. Defined for 0≤x≤ 10; relative maximum point at x = 3; absolute maximum value at x = 10 lative mini-