This activity introduces the notion of the gradient of a curve. Initial exploration involves a dynamic tangent where students can use prior knowledge of the gradient of a straight line to determine if the slope is negative, zero or positive. The second stage of the activity goes one step further by quantifying the gradient. The third stage sees the gradient function generated automatically including an opportunity to freely explore the relationship between a parabola and its gradient function. T
Interpret the derivative as the slope or gradient of a tangent line of the graph of y=f(x). [ ACMMM085 ]
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.