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

• 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

• 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

• 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.