question one

Use the gure below and the chain rule to estimate the derivative. The graph of f (x) has 3 Sharp corner at I : 2. 9' fir) Let H (I) = a if (Xi)- If the derivative does not exist, enter NA. {3] Find n\" m. rim: {In} Find if (x). [c] Find if (x). m = \fLet f(v) be the gas consumption (in liters/km) of a car going at velocity v (in km/hr). In other words, f(v) tells you how many liters of gas the car uses to go one kilometer, if it is going at velocity v. You are told that f(80) = 0.08 and f' (80) = 0.0009. (a) Let g(v) be the distance the same car goes on one liter of gas at velocity v. What is the relationship between f(v) and g(v)? Find g(80) and g' (80). (b) Let h(v) be the gas consumption in liters per hour. In other words, h(v) tells you how many liters of gas the car uses in one hour if it is going at velocity v. What is the relationship between h(v) and f(v)? Find h(80) and h' (80). 1.8'(v) = J (v) (f (0)2 : h (0) = f (v) - v . f' (v) 11. g' (v) = _ J (v) , h' (v) = f (v) + v. f' (v) (f (0 ) ) 2 Ill. g (v) = _ J (0) f (v) ,h' (v) = f (v) to. f' (v) IV. g' (v) = - f (v) f (v) , h' (v) = v . f' (v) Round to two decimal places. 8(80) = g' (80) = iA patient's total cholesterol level, T(t), and good cholesterol level, G(t), at t weeks after January 1, 2016, are measured in milligrams per deciliter of blood(mg/dl). The cholesterol ratio, R(t) = G(t)T(t) is used to gauge the safety of a patient's cholesterol, with risk of cholesterol-related illnesses being minimized when R(t) > 15 (that is, good cholesterol is at least 15 of total cholesterol). On January 1, the patient's total cholesterol level is 124 mg/dl and good cholesterol level is 35 mg/dl. Though R > 1/5, the doctor preferes that the patient's good cholesterol increase to 41 mg/dl, so prescribes a diet starting January 1 which increases good cholesterol by 1 mg/dl per week without changing the cholesterol ratio. What is the rate of change of total cholesterol the first week of the diet? Round to two decimal places. mg/dl per week(c) H(4) if H(x) = G(F(x)) H(4) = eTextbook and Media (d) H' (4) if H(x) = G(F(x)) H' (4) = i eTextbook and Media (e) H' (4) if H (x) = F(x) G(x) H' (4) = i