Students will be able to • Calculate the average rate of change ..., Summaries of Calculus

Download Students will be able to • Calculate the average rate of change ... and more Summaries Calculus in PDF only on Docsity! Rates of Change Objectives: Students will be able to • Calculate the average rate of change over an interval. • Calculate the instantaneous rate of change at a given point. We mentioned in the section on derivates that one main focus is rates of change. We will be looking at the average rate of change of a function over an interval and also the instantaneous rate of change of a function a specific point. In the case of the average rate of change, we will be finding the slope of the secant line through the end points of the interval. In the case of the instantaneous rate of change, we will once again be finding the derivative of the function at a point using the Newton’s Quotient and limits process. Example 1: Find the average rate of change between x = 1 and x = 3 for the function xxxf 2)( 2 += Example 2: Find the instantaneous rate of change at x = 1 for the function xxxf 2)( 2 += Example 3: Find the average rate of change between x = –2 and x = 1 for the function 1423)( 23 +−+−= xxxxf Example 4: Find the instantaneous rate of change at x = –2 for the function 1423)( 23 +−+−= xxxxf Example 5: Find the instantaneous rate of change at x = 2 for the function )ln( )( xxxf =