Average Rate of Change

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you calculate the average rate of change?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a), where [a, b] is the interval.

Front

What does a positive average rate of change indicate?

Back

It indicates that the function is increasing over the interval.

Front

What does a negative average rate of change indicate?

Back

It indicates that the function is decreasing over the interval.

Front

What is the average rate of change from 0 to 2 seconds if the distance traveled is 5 feet?

Back

Average Rate of Change = (5 - 0) / (2 - 0) = 2.5 feet per second.

Front

If a climber's altitude changes from 400 feet to 700 feet over 4 hours, what is the average rate of change?

Back

Average Rate of Change = (700 - 400) / (6 - 2) = 75 feet per hour.

Front

What is the significance of the interval in average rate of change?

Back

The interval determines the specific time frame over which the change is measured.

Front

How can you determine which interval has the largest average rate of change?

Back

Calculate the average rate of change for each interval and compare the values.

Front

What is the average speed of a vehicle that travels 120 miles in 2 hours?

Back

Average Speed = Total Distance / Total Time = 120 miles / 2 hours = 60 miles per hour.

Front

What is the average rate of change for the interval [13, 17] if the function values are 10 and 20?

Back

Average Rate of Change = (20 - 10) / (17 - 13) = 10 / 4 = 2.5.