Average Rate of Change

Example: Find the average rate of change of f(x) = 3x + 2 from x = 1 to x = 4.

• 1

• 2

• 3

• 4

How do you calculate the average rate of change?

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

• Average Rate of Change = (f(a) + f(b)) / 2, where [a, b] is the interval.

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

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

What does a positive average rate of change indicate?

• The function is decreasing over the interval.

• The function is constant over the interval.

• The function is increasing over the interval.

• The function has no change over the interval.

What is the average rate of change of the function y = 2(3)^x at the interval [2, 4]?

• 54

• 72

• 90

• 66

Example: If a car travels 60 miles in 1 hour, what is the average rate of change of distance with respect to time?

• 50 miles per hour

• 60 miles per hour

• 70 miles per hour

• 80 miles per hour

What is the average rate of change?

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

• The average rate of change is the maximum value of the function over the interval.

• The average rate of change is the minimum value of the function over the interval.

• The average rate of change is the sum of the function's values over the interval divided by the number of values.

How does the average rate of change relate to the derivative?

• The average rate of change is always equal to the derivative.

• The average rate of change over an interval approaches the derivative as the interval shrinks to a point.

• The average rate of change is the same as the instantaneous rate of change.

• The average rate of change can never be equal to the derivative.

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

• It means that the function's value does not change over the interval; it is constant.

• It means that the function is increasing over the interval.

• It means that the function is decreasing over the interval.

• It means that the function has a maximum or minimum value at some point in the interval.

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

• It varies depending on the function.

• It is equal to the y-intercept of the line.

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

• It is the difference in y-values divided by the difference in x-values.

What does a negative average rate of change indicate?

• The function is increasing over the interval.

• The function is constant over the interval.

• The function is decreasing over the interval.

• The function has no change over the interval.