Average Rate of Change

Front

What is the definition of 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 between two points (x1, y1) and (x2, y2)?

Back

The average rate of change is calculated using the formula: (y2 - y1) / (x2 - x1).

Front

What is the average rate of change from 20 to 40 minutes if the quantity decreases from 10 gallons to 0 gallons?

Back

The average rate of change is (-10 - 0) / (40 - 20) = -0.5 gallons per minute.

Front

If a function is increasing, what can be said about its average rate of change?

Back

If a function is increasing, its average rate of change is positive.

Front

If a function is decreasing, what can be said about its average rate of change?

Back

If a function is decreasing, its average rate of change is negative.

Front

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

Back

The average rate of change of a linear function is constant over any interval.

Front

How can the average rate of change be interpreted in a real-world context?

Back

In a real-world context, the average rate of change can represent speed, growth rate, or any other measure of change over time.

Front

What is the average rate of change of the function f(x) = 2x + 3 over the interval [1, 4]?

Back

The average rate of change is (f(4) - f(1)) / (4 - 1) = (11 - 5) / 3 = 2.

Front

What is the significance of the average rate of change in calculus?

Back

In calculus, the average rate of change is used to understand the behavior of functions and is a precursor to the concept of instantaneous rate of change.

Front

How does the average rate of change relate to the slope of a secant line?

Back

The average rate of change between two points on a graph is equivalent to the slope of the secant line that connects those two points.