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

If a function's average rate of change is zero, what does that mean?

Back

It means that the function's value does not change over the interval.

Front

Calculate 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

Find the average rate of change from 20 to 40 minutes if the gallons used changes from 10 to 0.

Back

Average Rate of Change = (0 - 10) / (40 - 20) = -0.5 gallons per minute.

Front

What is the average rate of change of the function f(x) = x^2 from x = 1 to x = 3?

Back

Average Rate of Change = (f(3) - f(1)) / (3 - 1) = (9 - 1) / 2 = 4.

Front

How can you interpret the average rate of change in a real-world context?

Back

It can represent speed, growth rate, or any change in quantity over time.

Front

What is the average rate of change of a linear function?

Back

For a linear function, the average rate of change is constant across all intervals.