Associate the verbal language of function behavior with characteristics of the graph of the function.
Elevator: Height and Velocity
Introduce ideas related to rectilinear motion.
Filling the Urn
Work with linked representations of the related rates of change of volume and height of fluid.
Higher Order Derivatives (CAS Tool)
Examine higher order derivatives using TI-Nspire Computer Algebra System (CAS).
Maximums, Minimums, and Zeroes
Determine when a function has a maximum or minimum based on the derivative of the function.
Visually see the geometry and calculus behind Newton's Method.
Students learn how to use the second derivative test to find maxima and minima in word problems and solve optimization in parametric functions.
Position, Distance, Velocity
Provide a position function to "drive" the rectilinear (straight line) horizontal motion of an object.
Students are given a situation of water draining out of a cylindrical tank in order to explain the process of solving related rates questions.
Roller Coaster Ride
Students visualize why the first derivative test works and how it is used to determine local minima and maxima.
The Classic Box Problem - Calculus
The Box_Problem_Calculus.tns document takes a classic problem from calculus and uses the dynamic linking capabilities of TI-Nspire to enact the problem in multiple representations: diagramatic, graphic, numeric, geometric, and symbolic. The problem is posed on the title screen shown at the right.
Xtreme Calculus: Part 1
Students explore relative maximums and minimums by dragging a tangent line to a curve and making observations about the slope of the tangent line.
Xtreme Calculus: Part 2
Students explore distance-time and velocity-time graphs to deepen their understanding of the application of the derivative.