Calculus Writing Assignment: Average Value of a Function Each problem is worth 5 points. Total Points: 75 Answer each of the problems. Make sure to show all your work. 1) Find the average value of the function f (x) = 3 - 4x + 5x 2 over the interval [1, 3]. 2) Find the average value of the function ln ( ) x g x x = over the interval [1, e]. 3) Find the average value of the function y(x) = 4 sec 2 x over the interval [0, /3]. 4) The area under the curve defined by the positive function f (x) on the interval [2, 6] is known to be 34. What is the average value of f (x) over the interval [2, 6]? 5) The function g(x) is always negative and has an average value of 12 over the interval 0 x 5. Find the area between the curve y = g(x) and the x-axis on the interval [0, 5]. 6) Write an expression that can be used to find the average rate of change in the function g(x) over the interval [4, 9]. 7) Write an expression that can be used to find the average value for the function g(x) over the interval [4, 9]. 8) Use the table of values below to find the average rate of change in f (x) over the interval 0 x 20. Show your calculations. x 0 5 10 15 20 f (x) 3 1 6 4 2 9) Use the table of values below to find the average value of f (x) over the interval 0 x 20. Show your calculations. x 0 5 10 15 20 f (x) 3 1 6 4 2 10) The graph of h(x) is shown below. Find the average value of h(x) over the interval [0, 10]. 11) Refer to the graph of h(x) in Problem 10. Find the average rate of change in h(x) over the interval [0, 10]. 12) The growth rate for a 24-hour period of a bacteria colony is measured to be r(t) = 96e 0.24t , where r(t) is measured in bacteria per hour. At t = 0, there are 400 bacteria in the colony. Find the average growth rate for the time period 0 t 24. Include units in your answer 13) Refer to the information in Problem 12. How many bacteria would be in the colony at the end of the 24-hour period? Round your answer to the nearest bacterium. 14) A student attempts to find the average value of y = x 1 on the interval [2, 2] using the following computation ( ) 2 1 2 1 2 ( 2) x dx . Is this accurate? Explain your reasoning. 15) Describe the difference in finding the average velocity over an interval given the position function, s