Average Rate of Change

Front

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.

Front

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 positive average rate of change indicate?

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?

Back

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

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

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

Back

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

Front

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

Back

Average Rate of Change = (f(4) - f(1)) / (4 - 1) = (11 - 5) / 3 = 2.

Front

What is the significance of the average rate of change in real life?

Back

It helps to understand how quantities change over time, such as speed, growth rates, and economic changes.

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How can the average rate of change be represented graphically?

Back

It can be represented as the slope of the secant line connecting two points on the graph of the function.

Front

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

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The average rate of change of a constant function is always 0, as the function's value does not change.