As we have seen, there are a couple of viewpoints to functions that drive our investigations.
One is a point-wise view. What is the function value at each domain number?
The other is a behavioral view. How are the function values changing?
We use these viewpoints when analyzing individual functions. We use these
viewpoints when comparing two functions. When comparing functions, it is not
enough to compare their values at each domain number. There are too many. We
need to move faster. We need to predict what is going to happen. That is where
rates-of-change come in.
We would like rates-of-change on intervals. We would also like a pointwise viewpoint
of rates-of-change.
A rate-of-change at a point seems like a contradiction, but fits in with the story of tangent lines very well.
Learning Outcomes
In this section, students will
- investigate rate of change.
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more examples can be found by following this link
More Examples of Rate of Change