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.
- 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?