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

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 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 of the function f(x) = 2x + 3 from x = 1 to x = 4?

Back

Average Rate of Change = (f(4) - f(1)) / (4 - 1) = (11 - 5) / 3 = 2.

Front

In the context of a graph, what does the average rate of change represent?

Back

The average rate of change represents the slope of the secant line connecting two points on the graph.

Front

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

Back

Average Rate of Change = (f(3) - f(2)) / (3 - 2) = (9 - 4) / 1 = 5.

Front

If a car travels 120 miles in 2 hours, what is the average rate of change in miles per hour?

Back

Average Rate of Change = 120 miles / 2 hours = 60 miles per hour.

Front

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

Back

For a linear function, the average rate of change is constant and equal to the slope of the line.

Front

How does the average rate of change differ from instantaneous rate of change?

Back

The average rate of change measures the change over an interval, while the instantaneous rate of change measures the change at a specific point.