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Example 1: Determine the average rate of change between the points (-6,-2) & (3,8).

Example 1: Determine the average rate of change between the points (-6,-2) & (3,8).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Chapter 1 - Rates of Change Lesson 1.1- Rates of Change and the Slope of a Curve Date: Rate of Change A measure of how rapidly the dependent variable changes when there is a change in the independent variable. There are two types of rates of change, average and instantaneous. • An average rate of change is a change that takes place over an interval. It is calculated by finding the slope of the secant joining the two endpoints of the interval. An instantaneous rate of change refers to the rate of change at a specific point (or at a particular instant). It corresponds to the slope of the tangent line at that particular point. • An estimate of the instantaneous rate of change can be obtained by calculating an average rate of change over the smallest interval for which data are available. • An estimate of instantaneous rate of change can also be determined using the slope of a tangent sketched on a graph. • However, both methods are limited by the accuracy of the data or the accuracy of the sketch. (That's why we have Calculus-yay! ☺)
Transcribed Image Text:Chapter 1 - Rates of Change Lesson 1.1- Rates of Change and the Slope of a Curve Date: Rate of Change A measure of how rapidly the dependent variable changes when there is a change in the independent variable. There are two types of rates of change, average and instantaneous. • An average rate of change is a change that takes place over an interval. It is calculated by finding the slope of the secant joining the two endpoints of the interval. An instantaneous rate of change refers to the rate of change at a specific point (or at a particular instant). It corresponds to the slope of the tangent line at that particular point. • An estimate of the instantaneous rate of change can be obtained by calculating an average rate of change over the smallest interval for which data are available. • An estimate of instantaneous rate of change can also be determined using the slope of a tangent sketched on a graph. • However, both methods are limited by the accuracy of the data or the accuracy of the sketch. (That's why we have Calculus-yay! ☺)
Lesson 1.1 Example 1: Determine the average rate of change between the points (-6,-2) & (3, 8). Example 2: a) Determine the average rate of change for -1≤x≤2. b) What is the instantaneous rate of change at x=1? t 0 1 2 3 4 5 6 7 P 800 34 6 799 782 737 652 515 314 37 4 Example 3: A new antibacterial spray is tested on a bacterial culture. The table shows the population, P, of the bacterial culture t, minutes after the spray is applied. Determine the average rate of change in the first 5 minutes. 2 (2,6) (-1,0) -4-2 0 2 4 x -2
Transcribed Image Text:Lesson 1.1 Example 1: Determine the average rate of change between the points (-6,-2) & (3, 8). Example 2: a) Determine the average rate of change for -1≤x≤2. b) What is the instantaneous rate of change at x=1? t 0 1 2 3 4 5 6 7 P 800 34 6 799 782 737 652 515 314 37 4 Example 3: A new antibacterial spray is tested on a bacterial culture. The table shows the population, P, of the bacterial culture t, minutes after the spray is applied. Determine the average rate of change in the first 5 minutes. 2 (2,6) (-1,0) -4-2 0 2 4 x -2
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