Average Rate of Change

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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.

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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.

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What does a negative average rate of change indicate?

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

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What does a positive average rate of change indicate?

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

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If a function has an average rate of change of 0, what does that mean?

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An average rate of change of 0 means that the function's value does not change over the interval.

Front

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

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

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How can you interpret the average rate of change in real-world scenarios?

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In real-world scenarios, the average rate of change can represent speed, growth rate, or any change over time.

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What is the average rate of change of a population from 1900 to 1990 if it increased from 75 million to 250 million?

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Average Rate of Change = (250 - 75) / (1990 - 1900) = 1.75 million people/year.

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What is the average rate of change of Pete's height if he grew from 36 inches to 48 inches between ages 3 and 5?

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Average Rate of Change = (48 - 36) / (5 - 3) = 6 inches per year.

Front

What is the significance of the interval when calculating average rate of change?

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The interval determines the specific values of the function being analyzed and affects the calculated rate.