Big Idea 2 from the 2016-2017 AP Calculus Curriculum Framework is Derivatives.
Enduring Understanding 2.1: The derivative of a function is defined as the limit of a difference quotient and can be determined using a variety of strategies.
Mathematical Practice for AP Calculus (MPAC) 2: Connecting Concepts
- relate the concept of a limit to all aspects of calculus
- Students can connect concepts to their visual representation with and without technology.
How do you introduce the definition of a derivative?
We start with the visual of a tangent line at a point and a secant line containing the point.
We don’t need calculus to determine the slope of the secant line. We do need calculus to determine the slope of the tangent line.
How might we use the slope of the secant line to determine the slope of the tangent line?