Question 1 Some values of a differentiable, invertible function f and its derivative are given below. I 0 2 4 6 | 8 f(2:) 15 13 10 s | 2 f'(:1:) 1 2 2.5 3 | 5 | Calculate the following. (a) Q\" (2), where g(:1:) : f(I)e3$_ (b) i116), where h(a;) = IBI(I)_ Question 2 A mass is hanging from the ceiling on a Spring and oscillating (forever, and without friction). At its highest point, the mass is 12 cm from the oor, and at its lowest point, the mass is 6 cm from the oor. At t = 0, the mass is at its equilibrium and moving downwards, and a single period takes 0.5 seconds. HINT: Graph your y(t) to check your answers. (a) Find a formula for y(t), the position of the mass from the oor as a function of time. (b) What is the position, velocity, and acceleration of the object at t = 2? (c) In its rst period, during what time interval(s) is the speed, |v|, of the mass less than 1 cm/s? Question 3 The fuel efciency of a car 13(3), in miles per gallon, is a function of the speed of the car .3, in miles per hour. Suppose that E (60) = 40 and BTW) = 0.7. (a) What are the units of E'(s)? (b) Let C(s) be the fuel consumption, in gallons per mile, of the car when it is driving 3 miles per hour. Find a formula for C(s) in terms of E(s). Calculate C'(60). (e) Let R(s), be the rate the car burns fuel, in gallons per hour, when the car is driving 3 miles per hour. Find a formula for R(s) in terms of E (3). Calculate R'(60). Question 4 Recall from Written Homework 1 that the average daily temperature (in Fahrenheit) in Portland, Maine is given by A(t) where t is the number of days after January 20. Furthermore the price of oil required to heat a home, 0 (measured in dollars per gallon) depends on the average daily temperature, A. (a) What is the meaning of O(A(0)) = 3.2 in the context of the problem? Be sure to include the units. (b) What is the meaning of g I A210 2 D.02 in the context of the problem? Be sure to include the units. . . d0 _ . (c) What is the meamng of E In the context of the problem? What are the units? (d) Recall from Written Homework 1 that the price of oil varied linearly with average daily temper ature where 0(A(t)) = 0.02A(t) + 3.5. Compute %. (Your answer may contain A and its derivative.) (e) Now recall that the average daily temperature varied sinusoidally over time so that A(t) = 46 2n d0 36 COS (t) . Compute E