# Derivatives

## Lesson plan, what is instantaneous rate of change for a function?

Idea: Every polynomial looks like a line, if you zoom close enough.
Earlier lessons. What is change? What is the the rate of change for a constant function? What is the rate of change for a linear function?
Earlier result: rate of change for a linear function is constant, (instantaneous rate of change is also a constant).
. Does it look like a line, if you zoom close?
Problem 3. Use the tangent tool in Geogebra and find out the instantaneous rate of change for a function when , and .
What is the general rule? Check, if your general rule holds, when .

**Tasks for students to solve in small groups, 2-3 in each.****Problem 1.**- With Geogebra, draw the graph of a function
. Zoom in close enough at any point. How does the graph look like? - When zoomed in, add two points to graph and draw a line through those points.
- Zoom out. What is the connection between the slope of the line and instantaneous rate of change of the function
at the point you zoomed in?

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