Two problems related to the mean-value theorem lead into a problem requiring the use of the universal chord theorem. This latter theorem is discussed and a proof given. (MP)

Pre- and posttests and interviews concerning misconceptions and alternate conceptions of rates of change were administered to (n=42) students in first-semester calculus using a conceptually-motivated curriculum. Suggests that an emphasis on visual representations through construction and interpretation in conjunction with teacher-student analysis…

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of…

Provides examples in which graphs are used in the statements of problems or in their solutions as a means of testing understanding of mathematical concepts. Examples (appropriate for a beginning course in calculus and analytic geometry) include slopes of lines and curves, quadratic formula, properties of the definite integral, and others. (JN)

This booklet contains a representative sample of the efforts of colleagues at 11 institutions to use graphing calculators to enhance the teaching of calculus and precalculus. The first section contains examples of graphs for teachers to choose from for presentations, including: simple examples to illustrate some standard ideas in precalculus,…

Theorems about the hyperbola which are ordinarily introduced in calculus courses can be proved without using the calculus. (SD)

Attempts to answer and generalize the question: When is the numerical derivative obtained on the graphing calculator greater than the actual derivative, and when is it smaller? Discusses symmetric difference. (MKR)

A transformation technique for graphing is described. (DT)

Curve stitching activities can be used to motivate calculus students. The problem described here involves showing that a given envelope of a curve is parabolic. (SD)

An examination of a student question concerning a calculus problem leads to a discussion of some of the symmetric properties of a specific set of polynomials. (MP)

This paper describes student difficulties in first-year calculus classes and suggests some instructional strategies to address these difficulties. Participants in this study were 200 low socio-economic background freshmen majoring in business in Brazil. Results show that the main difficulties are related to lack of understanding of algebraic…

Discussed is the method of substitution of variables within the framework of precalculus level extremum problems, both maximum and minimum. Many examples with graphical representations are provided. (JJK)

It is noted that all graphs of cubic equations are symmetric about their inflection points. This is proven through the use of some calculus and the fundamental theorem of algebra. A table sums up the nature of symmetry for polynomials of any degree. (MP)

Presented is a simple method which may be used to determine points of intersection in graphs of functions if they do exist. Several examples are given with illustrations of the functions. (CW)