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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.

Alignments  Standards  |  Textbook  
  • 3260

Derivative Analysis

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

Alignments  Standards  |  Textbook  
  • 5419

Maximums, Minimums, and Zeroes

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

Alignments  Standards  |  Textbook  
  • 5340


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

Alignments  Standards  |  Textbook  
  • 3284

Filling the Urn

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

Alignments  Standards  |  Textbook  
  • 5125

Elevator: Height and Velocity

Introduce ideas related to rectilinear motion.

Alignments  Standards  |  Textbook  
  • 4891

Position, Distance, Velocity

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

Alignments  Standards  |  Textbook  
  • 5081

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.

Alignments  Standards  |  Textbook  
  • 3632

Higher Order Derivatives (CAS Tool)

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

Alignments  Standards  |  Textbook  
  • 5008

Newton's Method

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

Alignments  Standards  |  Textbook  
  • 5331

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.

Alignments  Standards  |  Textbook  
  • 2813

Xtreme Calculus: Part 2

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

Alignments  Standards  |  Textbook  
  • 2673

Roller Coaster Ride

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

Alignments  Standards  |  Textbook  
  • 2636
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