Page of 10 0 - ZOOM + Press Esc to exit full screen Name: MATH 172 HW Week 2, Duc: July 5 at 11:59 pm Summer 2022 1. Suppose that y = f(r) is a function for which three values are known: [1] f(10) = 25, f(20) = 32.5 and f(30) = 36.25. Use central difference to estimate f'(20). 2. A potato is placed in an oven, and the potato's temperature F (in degrees Fahrenheit) at various points in time is taken and recorded in the following table. Time t is measured in minutes. Table: Temperature data in degrees Fahrenheit. 10 20 F(t) 70 180 250 290 320 340 350 a. Use a central difference to estimate the instantaneous rate of change of the temper- ature of the potato at t = 30. Include units on your answer. [1]Page of 10 0 - ZOOM + Name: MATH 172 HW Week 2, Duc: July 5 at 11:59 pm Summer 2022 1. Suppose that y = f(r) is a function for which three values are known: [1] f(10) = 25, f (20) = 32.5 and f(30) = 36.25. Use central difference to estimate f'(20). 2. A potato is placed in an oven, and the potato's temperature F (in degrees Fahrenheit) at various points in time is taken and recorded in the following table. Time t is measured in minutes. Table: Temperature data in degrees Fahrenheit. 10 20 F(t) 70 180 250 290 320 340 350 a. Use a central difference to estimate the instantaneous rate of change of the temper- ature of the potato at t = 30. Include units on your answer. [1]Page of 10 0 ZOOM + b. Use a central difference to estimate the instantaneous rate of change of the temper- ature of the potato at t = 50. Include units on your answer. [1] c. Without doing any calculation, which do you expect to be greater: F'(50) or F"(60) ? Why? [1] 3. A company manufactures rope, and the total cost of producing a feet of rope is C(I) dollars. a. What does it mean to say that C(200) = 80 ? [1]Page of 10 0 ZOOM + b. What are the units of C'(x) ? [1] c. Suppose that C(200) = 80 and C"(200) = 0.35. Estimate C(250), and justify your estimate by writing at least one sentence that explains your thinking. [1] 4. Researchers at a major car company have found a function that relates gasoline con- sumption to speed for a particular model of car. In particular, they have determined that the consumption C, in liters per kilometer, at a given speed s, is given by a function C = f(s), where s is the car's speed in kilometers per hour. a. Data provided by the car company tells us that f(50) = 0.15, f(60) = 0.2, and f(70) = 0.27. Use this information to estimate the instantaneous rate of change of fuel consumption with respect to speed at s = 60. Be as accurate as possible, use proper notation, and include units on your answer. [1]Page of 10 - ZOOM + b. By writing a complete sentence, interpret the meaning (in the context of fuel consumption) of "f(50) = 0.15." [1] c. Write at least one complete sentence that interprets the meaning of the value of f'(60) that you estimated in (a). [1]