Q25,Q27,Q29&Q31 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 I am repeating solve all in the order to get positive feedback 2.2 The First- and Second-Derivative Rules 147Exercises 25-36 refer to Fig. 23, which contains the graph of '(x). 41. By looking at the second derivative, decide which of thethe derivative of the function f(x).curves in Fig. 25 could be the graph of f(x)=x5/2M3+2140/1-1+-21v=J'(x)Figure 2325. Explain why f(x) must be increasing at x = 6.26. Explain why f(x) must be decreasing at x = 4.27. Explain why f(x) has a relative maximum at x = 3.28. Explain why f(x) has a relative minimum at x = 5.29. Explain why f(x) must be concave up at x = 0.30. Explain why f(x) must be concave down at x = 2.31. Explain why f(x) has an inflection point at x = 1.32. Explain why f(x) has an inflection point at x = 4.utod lo sgada luneusFigure 242 333. If f(6)=3, what is the equation of the tangent line to thegraph of y=f(x) at x = 6?34. If f(6)= 8, what is an approximate value of f(6.5)?35. If f(0) = 3, what is an approximate value of f(.25)?Y4/536. If f(0) = 3, what is the equation of the tangent line to thegraph of y=f(x) at x = 0?I37. Level of Water from Melting Snow Melting snow causes a riverto overflow its banks. Let h(t) denote the number of inches ofwater on Main Street r hours after the melting begins.(a) If h'(100)=, by approximately how much will the waterlevel change during the next half hour?(b) Which of the following two conditions is the better news?(i) h(100) = 3, h'(100) = 2, h"(100) = -5(ii) h(100) = 3, h'(100) = -2, h"(100) = 538. Changes in Temperature T(t) is the temperature on a hotsummer day at time / hours.og muniat(a) If T'(10) = 4, by approximately how much will the tem-perature rise from 10:00 to 10:45?(6,2)+6(b) Which of the following two conditions is the better newsif you do not like hot weather? Explain your answer.(i) T(10) = 95, T'(10) = 4, T"(10) = -3(ii) T(10) = 95, T'(10) = -4, 7"(10) = 339. Decide which of the curves in Fig. 24 could not be the graphof f(x) = (3x² + 1) for x ≥ 0. Decide which of the curves inFig. 24 could not be the graph of f(x) = (3x² + 1)4 for x ≥ 0by considering the derivative of f(x). Explain your answer.Yto playIIxde-Figure 2542. Match each observation (a)-(e) with a conclusion (A)-(E).Observations(a) The point (3, 4) is on the graph of f'(x).(b) The point (3, 4) is on the graph of f(x).(c) The point (3, 4) is on the graph of f(x).(d) The point (3, 0) is on the graph of f'(x), and the point(3, 4) is on the graph of f(x).(e) The point (3, 0) is on the graph of f'(x), and the point(3,-4) is on the graph of f"(x).Conclusions(A) f(x) has a relative minimum point at x = 3.(B) When x = 3, the graph of f(x) is concave up.(C) When x = 3, the tangent line to the graph of y=f(x)has slope 4.(D) When x = 3, the value of f(x) is 4.(E) f(x) has a relative maximum point at x = 3.00392priroleabivosbe noirerond -.0543. Number of Farms in the U.S. The number of farms in theUnited States / years after 1925 is f(t) million, where is thefunction graphed in Fig. 26(a). [The graphs of f'(t) and f"(t)are shown in Fig. 26(b).]6543210(1925)201yلال10 20 3040. By looking at the first derivative, decide which of the curves inFig. 24 could not be the graph of f(x)= x³9x² + 24x + 1 om to and domibusfor x ≥ 0. [Hint: Factor the formula for f'(x).]Figure 26x11y=f(t)t30 40 50 60 70(a)(b)10 20 30 40 50 60 70+1y=J")y=f'(0)newhenE.S

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Q25,Q27,Q29&Q31 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 I am repeating solve all in the order to get positive feedback 2.2 The First- and Second-Derivative Rules 147Exercises 25-36 refer to Fig. 23, which contains the graph of '(x). 41. By looking at the second derivative, decide which of thethe derivative of the function f(x).curves in Fig. 25 could be the graph of f(x)=x5/2M3+2140/1-1+-21v=J'(x)Figure 2325. Explain why f(x) must be increasing at x = 6.26. Explain why f(x) must be decreasing at x = 4.27. Explain why f(x) has a relative maximum at x = 3.28. Explain why f(x) has a relative minimum at x = 5.29. Explain why f(x) must be concave up at x = 0.30. Explain why f(x) must be concave down at x = 2.31. Explain why f(x) has an inflection point at x = 1.32. Explain why f(x) has an inflection point at x = 4.utod lo sgada luneusFigure 242 333. If f(6)=3, what is the equation of the tangent line to thegraph of y=f(x) at x = 6?34. If f(6)= 8, what is an approximate value of f(6.5)?35. If f(0) = 3, what is an approximate value of f(.25)?Y4/536. If f(0) = 3, what is the equation of the tangent line to thegraph of y=f(x) at x = 0?I37. Level of Water from Melting Snow Melting snow causes a riverto overflow its banks. Let h(t) denote the number of inches ofwater on Main Street r hours after the melting begins.(a) If h'(100)=, by approximately how much will the waterlevel change during the next half hour?(b) Which of the following two conditions is the better news?(i) h(100) = 3, h'(100) = 2, h&#34;(100) = -5(ii) h(100) = 3, h'(100) = -2, h&#34;(100) = 538. Changes in Temperature T(t) is the temperature on a hotsummer day at time / hours.og muniat(a) If T'(10) = 4, by approximately how much will the tem-perature rise from 10:00 to 10:45?(6,2)+6(b) Which of the following two conditions is the better newsif you do not like hot weather? Explain your answer.(i) T(10) = 95, T'(10) = 4, T&#34;(10) = -3(ii) T(10) = 95, T'(10) = -4, 7&#34;(10) = 339. Decide which of the curves in Fig. 24 could not be the graphof f(x) = (3x² + 1) for x ≥ 0. Decide which of the curves inFig. 24 could not be the graph of f(x) = (3x² + 1)4 for x ≥ 0by considering the derivative of f(x). Explain your answer.Yto playIIxde-Figure 2542. Match each observation (a)-(e) with a conclusion (A)-(E).Observations(a) The point (3, 4) is on the graph of f'(x).(b) The point (3, 4) is on the graph of f(x).(c) The point (3, 4) is on the graph of f(x).(d) The point (3, 0) is on the graph of f'(x), and the point(3, 4) is on the graph of f(x).(e) The point (3, 0) is on the graph of f'(x), and the point(3,-4) is on the graph of f&#34;(x).Conclusions(A) f(x) has a relative minimum point at x = 3.(B) When x = 3, the graph of f(x) is concave up.(C) When x = 3, the tangent line to the graph of y=f(x)has slope 4.(D) When x = 3, the value of f(x) is 4.(E) f(x) has a relative maximum point at x = 3.00392priroleabivosbe noirerond -.0543. Number of Farms in the U.S. The number of farms in theUnited States / years after 1925 is f(t) million, where is thefunction graphed in Fig. 26(a). [The graphs of f'(t) and f&#34;(t)are shown in Fig. 26(b).]6543210(1925)201yلال10 20 3040. By looking at the first derivative, decide which of the curves inFig. 24 could not be the graph of f(x)= x³9x² + 24x + 1 om to and domibusfor x ≥ 0. [Hint: Factor the formula for f'(x).]Figure 26x11y=f(t)t30 40 50 60 70(a)(b)10 20 30 40 50 60 70+1y=J&#34;)y=f'(0)newhenE.S

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