# 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). Tasks for students to solve in small groups, 2-3 in each. Problem 1.
1. With Geogebra, draw the graph of a function . Zoom in close enough at any point. How does the graph look like?
2. When zoomed in, add two points to graph and draw a line through those points.
3. 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?
Problem 2. Study the graph of the function . 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 .