- Derivatives and Graphing
- Tutorial on using the derivative to detect increasing and decreasing functions. Local maximum and local minimum are also defined. Emphasis on graphical analysis.
- Tutorial on using the second derivative to detect concavity of functions. Inflection points are also defined. Emphasis on graphical analysis.
- A LiveMath Notebook that draws the graph of a function and its second derivative.
- Computer programs that draw the graph of a function and its second derivative. Also,
- Computer programs that draw the graph of a function and its second derivative.
- Quiz which tests the ability to determine graphically information about a function and its derivatives.
- Quiz which tests the ability to determine information
about the graph of a function from information about its derivatives.
- Quiz on determining which graph is the graph of a function, its derivative and its 2nd derivatives.
- Tangent Lines and Parametric Curves
- Tutorial on finding tangent lines to parametric curves.
- A LiveMath Notebook illustrating the finding of the equation
of a tangent line to a parametric curve.
- Drill problems on finding the derivative and the equation of the tangent line to a parametric curve.
- Using the TI-85 Graphing Calculator to find and graph the tangent line to a parametric curve. Also,
- Tutorial on finding tangent lines to polar curves.
- Implicit Differentiation
- Tutorial on implicit differentiation.
- Drill on finding the derivative and the equation of the tangent line at a given point.
- Drill problems for finding a derivative by implicit differentiation.
- A LiveMath Notebook illustrating implicit differentiation.
- Computer programs that plot the graph of a relation and calculate the derivative.
- Computer programs that plot the graph of a relation and tangent lines at various points.
- Computer programs that plot the graphs of a family of hyperbolas and an orthogonal family of hyperbolas.
- Derivatives of Inverse Functions
- Tutorial on finding the derivatives of inverse functions.
- Drill on finding the derivative and the tangent line to the inverse of a function.
- Logarithmic Differentiation
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- Drill on applying logarithmic differentiation.
- Derivatives and Inverses of Trigonometric Functions
- Tutorial on finding the derivatives of the inverse trig functions.
- Differentials
- Tutorial on differentials.
- Drill on using differentials to approximate expressions.
- Maxima and Minima
- Tutorial on finding the maxima and minima of a function on a closed interval.
- Drill on finding the maxima and minima of a function on a closed interval.
- L'Hospital's Rule
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- Drill on applying L'Hospital's Rule. (Using finite limits)
- Drill on applying L'Hospital's Rule. (Using infinite limits)
- Mean Value Theorem
- Tutorial on the Mean Value Theorem; includes Rolle's Theorem and the First Derivative Test.
- Drill on applying the Mean Value Theorem.
- Drill on using the First Derivative Test.
- Drill on determining the intervals of concave upward and concave downward
and the inflection points of a function.
- Computer programs that can be used to illustrate the Mean Value Theorem. Also,
- Optimization Problems
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- Java applets illustrating the solution to finding the maximum area of a rectangle which can be inscribed in a semicircle.
- Java applet illustrating the solution to finding the longest ladder which can be carried through a hallway with a corner.
- Java applet illustrating the solution to finding the shortest time to move through the desert to a town.
- Java applet illustrating the solution to finding the shortest
ladder that can lean over a fence against a building.
- Newton's Method
- Tutorial on Newton's Method.
- Drill problems on the use of Newton's Method.
- Computer programs that numerically illustrate the use of Newton's Method.
- Computer programs that graphically illustrate the use of Newton's Method.
- Computer programs that Graphically illustrate the use of Newton's Method and the problems with using Newton's Method.