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Home > AP Courses and Exams > Course Home Pages > Applications of the Derivative

Applications of the Derivative

Applications of Differentiation
Scroll to the bottom of this page and you will find four nice applets illustrating some standard optimization problems. With the exception of the first, they are interactive, allowing you to change the parameter and guess the optimum value. After the demonstration, there is a complete step-by-step solution for the problem. These would make a good introduction to a class on optimization.
  Applications of Differentiation

Applications of Maxima and Minima
This is a short tutorial explaining how to set up and solve optimization problems. There is one "real world" example and two "not so real world" examples. The reader is led through the steps of the solution with interactive questions. This would be a good place to review the procedure for solving an optimization problem.
  Applications of Maxima and Minima

Graphs and Second Derivatives
This brief tutorial presents the relationship between the graph of a function, its second derivative, and its concavity. There is a clear discussion of the definitions as well as interactive applets that allow the viewer to see different graphs and their first and second derivatives. At the end of the tutorial are three very different, and very good, interactive quizzes that are worth looking at.
  Graphs and Second Derivatives

Applications of Derivatives
This page is part of a site maintained by Sandra Halfacre of White Station High School in Memphis, Tennessee. It contains links to tutorials, slide shows, animations, and applets involving applications of derivatives, including rectilinear motion, curve sketching, min/max, local linearity, and related rates.
  Applications of Derivatives

Linear Approximations
This is a short tutorial on linear approximations of a function, concentrating on the error in the approximation. It includes a list of objectives, a discussion (using an analytic approach), and four applets illustrating the error numerically and graphically. The animations are interactive and run smoothly. (They require Macromedia's Flash 5 Player or LiveMath plug-ins, which can be downloaded free.)
  Linear Approximations

Linear Approximation and Error Estimation
A good tutorial for the concept of local linearity.
  Linear Approximation and Error Estimation

Related Rates
This short tutorial explains the steps involved in solving a related rate problem. There are two interactive examples (a circle whose radius is increasing and the ladder-sliding-down-a-wall problem) separated by a discussion of the steps to follow and the reasons behind them.
  Related Rates

Mean Value Theorem
The progression from Rolle's Theorem to the Mean Value Theorem (MVT) to increasing and decreasing functions and the First Derivative Test for Extrema is covered in this tutorial. Each part has an applet explaining the reasoning behind the theorem. There are drill problems with graphs and step-by-step solutions on the MVT and on the First Derivative Test.
  Mean Value Theorem







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