Minimum, Maximum, First and Second Derivatives. A tutorial on how to use calculus theorems using first and second derivatives to determine whether a function has a relative maximum or minimum or neither at a given point.
Newton's Method to Find Zeros of a Function. Newton's method is an example of how differentiation is used to find zeros of functions and solve equations numerically. Examples with detailed solutions on how to use Newton s method are presented.
Linear Approximation of Functions. Linear approximation is another example of how differentiation is used to approximate functions by linear ones close to a given point. Examples with detailed solutions on linear approximations are presented.
Find Critical Numbers of Functions. Tutorial on how to find the critical numbers of a function. Several examples with detailed solutions and exercises with answers.
Derivative, Maximum, Minimum of Quadratic Functions. Differentiation is used to analyze the properties such as intervals of increase, decrease, local maximum, local minimum of quadratic functions. Examples with solutions and exercises with answers.
Find Area Under Curve. How to find the area under (and between) curves using definite integrals; tutorials, with examples and detailed solutions are presented.
Find The Volume of a Solid of Revolution. How to find the volume of a solid of revolution generated by revolving a region bounded by the graph of a function around one of the axes using definite integrals?
Volume by Cylindrical Shells Method. Find the volume of a solid of revolution generated by revolving a region bounded by the graph of a function around one of the axes using cylindrical shells.
Maxima and Minima of Functions of Two Variables. Locate relative maxima, minima and saddle points of functions of two variables. Several examples with detailed solutions are presented. 3-Dimensional graphs of functions are shown to confirm the existence of these points.
Optimization Problems with Functions of Two Variables. Several optimization problems are solved and detailed solutions are presented. These problems involve optimizing functions in two variables using first and second order partial derivatives..