Average Rate of Change Over an Interval

Average Rate of Change Over an Interval

Finding Average Rate of Change

• When finding the average rate of change over an interval, we are looking to find the slope.

• Make sure that you pay attention to scales on your graphs.

• If you have to, you can find points using inputs and outputs.

What is going on with this graph?

Where is she traveling the fastest? How do you know?

Where is she traveling the slowest? How do you know?

Multiple Choice

Which of the following intervals has the largest average rate of change?

• [13,14]

• [13, 17]

• [16, 17]

• [16, 19]

What happens though when the graph doesn't have linear parts?

• Find the Rate Of Change over a given interval

• Notice: the rate of change over [0,1] is different than the rate of change over [1,2]

Find the Rate of Change over [-2,0]

• Identify the interval.

• Use the graph to find the ROC.

Multiple Choice

Find the average rate of change over the given interval.

• 4

• 7

• 7/3

• 3/7

Multiple Choice

Use the graph to find the average rate of change over the interval

• -1

• 1

• 1/2

• 2

Finding AROC from an equation

• The ball is traveling according to the function below. Find the average speed of the ball between 0 and 6 seconds

Find AROC

• A rock is dropped from a bridge. The distance the rock travels can be modeled by the function below. Find the average speed that the rock travels between 5 and 10 seconds?  

Multiple Choice

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

• 2
• 1/2
• -2
• -1/2

Multiple Choice

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

• 2
• 1/2
• -2
• -1/2

Open Ended

Find the average rate of change over the given interval.

 $f\left(x\right)=3x^2-x-2\ \left[-1,4\right]$  

Open Ended

Find the average rate of change over the given interval.

 $f\left(x\right)=3x^{2\ }-x-2;\ \left[4,7\right]$