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

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 speed?

Back

Average speed is the total distance traveled divided by the total time taken.

Front

If a car travels 100 miles in 2 hours, what is its average speed?

Back

Average Speed = Total Distance / Total Time = 100 miles / 2 hours = 50 miles per hour.

Front

What is the significance of the slope in a distance-time graph?

Back

The slope of a distance-time graph represents the average speed of the object.

Front

How can you determine the interval with the greatest average rate of change from a graph?

Back

Look for the steepest slope on the graph over the given intervals.

Front

What is the average rate of change from 0 to 5 if f(0) = 2 and f(5) = 12?

Back

Average Rate of Change = (12 - 2) / (5 - 0) = 10 / 5 = 2.

Front

What is the average rate of change from 10 to 20 if f(10) = 30 and f(20) = 10?

Back

Average Rate of Change = (10 - 30) / (20 - 10) = -20 / 10 = -2.