12/09 & 12/10 HW: 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 f(b) and f(a) are the function values at points b and a.

Front

What does a positive average rate of change indicate?

Back

A positive average rate of change indicates that the function is increasing over the interval.

Front

What does a negative average rate of change indicate?

Back

A negative average rate of change indicates that the function is decreasing over the interval.

Front

What is the average rate of change in profit if the profit increases from $100 to $300 over 10 hours?

Back

Average Rate of Change = (300 - 100) / (10 - 0) = 20 dollars per hour.

Front

If a family travels 204 miles in 3 hours, what is their average rate of change in miles per hour?

Back

Average Rate of Change = (204 - 0) / (3 - 0) = 68 miles per hour.

Front

What is the significance of the average rate of change in real-life scenarios?

Back

It helps in understanding how quantities change over time, such as speed, profit, or population growth.

Front

What is the average rate of change between the points (2, 4) and (6, 16)?

Back

Average Rate of Change = (16 - 4) / (6 - 2) = 3.

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.

Front

How does the average rate of change relate to the slope of a line?

Back

The average rate of change between two points on a line is equal to the slope of that line.