Objectives
Interpret the derivative as the slope or gradient of a tangent line of the graph of y=f(x).
Vocabulary
- Gradient
- Slope
- Steepness
- Tangent
- Sign
About the Lesson
In stage one of this activity students use the interactive features of TI-Nspire to explore gradient via a tangent line determining if the gradient is negative, zero or positive. This information is used to complete a sign table as a lead in to stage two where the gradient is quantified and subsequently graphed by consideration of a set of points. In the final stage students can freely explore a quadratic function and identify relationships between the original function and its gradient function.