Average Rate of Change

Front

What is the average rate of change (ARC)?

Back

The average rate of change (ARC) of a function over an interval [x1, x2] is defined as the change in the function's value divided by the change in the input value, calculated as (f(x2) - f(x1)) / (x2 - x1).

Front

How do you calculate the average rate of change for the function f(x) = 2x^2 + 12x + 16 on the interval [-3, -2]?

Back

First, calculate f(-3) and f(-2). Then, use the formula ARC = (f(-2) - f(-3)) / (-2 - (-3)). The result is 2.

Front

What is the formula for average rate of change?

Back

The formula for average rate of change is (y2 - y1) / (x2 - x1).

Front

If f(x) = x^2, what is the average rate of change from x = 1 to x = 3?

Back

The average rate of change is (f(3) - f(1)) / (3 - 1) = (9 - 1) / (3 - 1) = 4.

Front

What does a positive average rate of change indicate about a function?

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 about a function?

Back

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

Front

If the average rate of change is zero, what can be inferred about the function?

Back

If the average rate of change is zero, it indicates that the function's value does not change over the interval, suggesting it is constant.

Front

Calculate the average rate of change of f(x) = 3x + 4 from x = 2 to x = 5.

Back

ARC = (f(5) - f(2)) / (5 - 2) = (19 - 10) / 3 = 3.

Front

What is the average rate of change of f(x) = -x^2 + 4 on the interval [0, 2]?

Back

ARC = (f(2) - f(0)) / (2 - 0) = (0 - 4) / 2 = -2.

Front

How can you determine which of two functions has a greater average rate of change over an interval?

Back

Calculate the average rate of change for both functions over the same interval and compare the results.