Lesson 4.7 - 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.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

If a squirrel runs up a tree slowly, what can we say about the average rate of change of its height?

Back

The average rate of change is small and positive.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

What does a negative average rate of change indicate?

Back

It indicates that the function's value is decreasing over the interval.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

How can you determine if the average rate of change is positive, negative, or zero?

Back

By comparing the function's values at the endpoints of the interval.

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CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

What does it mean if the average rate of change is zero?

Back

It means that the function's value does not change over the interval.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

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.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

What does a positive average rate of change indicate?

Back

It indicates that the function's value is increasing over the interval.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

In the context of temperature, what does a negative average rate of change from n = 1 to n = 5 mean?

Back

It means the temperature decreased during that time period.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

If a person walks faster between 80 and 100 seconds than between 20 and 40 seconds, what can we infer about the average rates of change?

Back

The average rate of change is greater between 80 and 100 seconds.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

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

Back

The interval determines the specific values of the function that are used to calculate the change.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4