Calculus

Applications of the Derivative

This unit considers the use of the derivative in extensions and applications, including graphical analysis, applications to the study of motion (position and velocity), related rates, and optimization (max-min) problems. An application of the derivative to finding zeroes of functions (Newton’s Method) is also included.

Calculus: Applications of the Derivative Activities

Title Type

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.

• 3313

Derivative Analysis

Associate the verbal language of function behavior with characteristics of the graph of the function.

• 5448

Maximums, Minimums, and Zeroes

Determine when a function has a maximum or minimum based on the derivative of the function.

• 5377

Optimization

Students learn how to use the second derivative test to find maxima and minima in word problems and solve optimization in parametric functions.

• 3314

Filling the Urn

Work with linked representations of the related rates of change of volume and height of fluid.

• 5152

Elevator: Height and Velocity

Introduce ideas related to rectilinear motion.

• 4919

Position, Distance, Velocity

Provide a position function to "drive" the rectilinear (straight line) horizontal motion of an object.

• 5113

Relating Rates

Students are given a situation of water draining out of a cylindrical tank in order to explain the process of solving related rates questions.

• 3675

Higher Order Derivatives (CAS Tool)

Examine higher order derivatives using TI-Nspire Computer Algebra System (CAS).

• 5036

Newton's Method

Visually see the geometry and calculus behind Newton's Method.

• 5368

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.

• 2842

Xtreme Calculus: Part 2

Students explore distance-time and velocity-time graphs to deepen their understanding of the application of the derivative.

• 2697

Roller Coaster Ride

Students visualize why the first derivative test works and how it is used to determine local minima and maxima.

• 2673