need help with the following

. . . X 2.3 (b) What is the practical meaning of S'(t) > 0? What circumstances might cause this situation? 6. An economist is interested in how the price of a certain item affects its sales. At a price of $p, a quantity, q, of 30. For a function f(x), we know that f(20) = 68 and f '(20) = -3. Estimate f(21), f(19) and f(25). the item is sold. If q = f(p), explain the meaning of each of the following statements: In Problems 32,36, use the tangent line approximation. (a) f(150) = 2000 32. Given f(4) = 5, f '(4) = 7, approximate f(3.92). (b) f '(150) = -25 36. Given f(3) = -4, f '(3) = -2 approximate f(2.99). 8. The cost, C = f(w), in dollars of buying a chemical is a function of the weight bought, w, in pounds. in Problem 40 concern g(t) in Figure 2.35, which gives the weight of a human fetus as a function of its age. (a) In the statement f(12) =5, what are the units of the 12? What are the units of the 5? Explain what this is saying about the cost of buying the chemical. weight (kg) (b) Do you expect the derivative f' to be positive or negative? Why? w g(t) (c) In the statement f'(12) = 0.4, what are the units of the 12? What are the units of the 0.4? Explain what this is N saying about the cost of buying the chemical. 10. Figure 2.34 shows the power output, p(w), of a wind turbine as a function of wind speed, w. 1, age of fetus 16 24 32 40 (weeks after last menstruation) power (watts) Figure 2.35 p(w) 50,000 40,000 40. (a) Which is greater, g '(20) or g '(36)? 30,000 (b) What does your answer say about fetal growth? 20,000 10,000 5 10 15 20 w (m/sec) End of document Figure 2.34 (a) At what wind speed does the turbine generate the most power? (b) The derivative p '(7) is positive but the derivative p '(15) is negative. What does this tell you? (c) Give units and interpret p(7) = 17,500 and p '(7) = 8000. (d) Give units and interpret p(15) = 50,000 and p '(15) = -800. 16. Let S(t) be the amount of water, measured in acre-feet, that is stored in a reservoir in week t. (a) What are the units of S '(t)