Average Rate of Change

Front

What is the average rate of change of a function f(x) on the interval [a, b]?

Back

The average rate of change of a function f(x) on the interval [a, b] is given by the formula: (f(b) - f(a)) / (b - a).

Front

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

Back

First, calculate f(-3) and f(-2). Then use the formula: (f(-2) - f(-3)) / (-2 - (-3)). The answer is 2.

Front

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

Back

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

Front

What does a negative average rate of change indicate about a function on an interval?

Back

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

Front

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

Back

Calculate f(1) and f(2), then use the formula: (f(2) - f(1)) / (2 - 1). The answer is 9.

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 can you find the average rate of change using a graph?

Back

To find the average rate of change using a graph, identify two points on the curve, (x1, y1) and (x2, y2), and use the formula: (y2 - y1) / (x2 - x1).

Front

What is the significance of the average rate of change in real-world applications?

Back

The average rate of change can represent speed, growth rate, or any change in quantity over time, making it useful in various real-world contexts.

Front

What is the average rate of change of Mrs. Gordon's movement from 0 to 2 seconds if she travels 5 feet?

Back

The average rate of change is calculated as distance/time = 5 feet / 2 seconds = 2.5 feet per second.

Front

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

Back

The average rate of change of a constant function is always 0, as there is no change in output regardless of the input.