Rate of change problems pdf

Activity 1.1 - Average Rate of Change FOR DISCUSSION: In your own words, describe the major aspects of the graph shown below. 1. Suppose the function y f(x) represents a town's daily high temperature in degrees Celsius, where x is the number of days since New Year's Day, -3 < x < 5 (x = 0 corresponds to January 1). (a) On which interval(s) was the temperature above Change, Percent Change, and Average Rate of Change Change is the difference between the values of a quantity over a given interval. The interval does not have to be a time interval, but it is convenient to think of it for our initial examples. If the population of a region starts at 150 and ends at 165, the population changes by 15. We find this value by taking the final quantity and , and simplify. This resulting expression will tell the average rate of change between any two points on the function that are exactly 3 units apart. Hint to finish problem 1 : To find the average rate of change between two points, use the left endpoint as " " in the difference quotient. 1 x 2 x Average rate of change -4 -1 -2 1 0 3 Math Algebra 1 Functions Average rate of change word problems. Average rate of change word problem: table. Average rate of change word problem: graph. Practice: Average rate of change word problems. Average rate of change review. For both of these functions the rate of change is 3. That means the outputs grow by 3 when the inputs are consecutive. 3 Ask your students if the rate of change of 3 is visible anywhere else, aside from the constant change in the outputs. We want them to notice that the rate of change appears in two places: the table and the rule. Linear rate of change: Steady growth ʅ Click the link above to launch the map. ʅ With the Details button depressed, click the button, (Show) Contents.? Which Michigan county looks like it has the highest population? [Answers may include Macomb, Kent, Genesee, Oakland, or Wayne.] ʅ Click a county with a high population in 2010 to see a pop-up. Problem 6 a) Use either limit definition of the derivative to find) (a f c if 1) (² x x x f b) Find ´ µ 1 f c, ´ µ 2 f c, ´ µ 3 f Problem 7 Using the limit definition of the derivative, find the instantaneous rate of change of the following functions at x = 2. a) 2 1) (x x g b) ´ µ x x h S sin) (. c. For each problem, find the average rate of change of the function over the given interval. 1) f ( x ) x x ; [ , x The purpose of this Collection of Problems is to be an additional learning resource for students who are taking a di erential calculus course at Simon Fraser University. The Collection contains problems given at Math 151 - Calculus I and Math 150 - Calculus I With Review nal exams in the period 2000-2009. The problems are 9.3 Average and Instantaneous Rates of Change: The Derivative 609 Average Rate of Change Average and Instantaneous Rates of Change: The Derivative] Application Preview In Chapter 1, "Linear Equations and Functions," we studied linear revenue functions and defined the marginal revenue for a product as the rate of change of the revenue function. Solve the problem. 13) A particular strain of influenza is known to spread according to the function p(t) = 1 2 (t2 + t), where t is the number of days after the first appearance of the strain and p(t) is the percentage of the population that is infected. Find the instantaneous rate of change of p with respect to t at t = 3. A) 6% per day B) 7 2 The velocity problem Tangent lines Rates of change Rates o