Discussion 14: Contour Plots

The goal of this discussion is to have the students to analyze a contour plot of Doublehead Mountain in New Hampshire in order to determine what they can learn about a function, in this case an altitude function, from its contour plot. Students should be familiar with the contour plot of a function of two variables.

The first exercise asks students to focus on the local maxima on the plot and to describe the contours near a maximum point. In the second and third exercises, students are asked to consider different paths on the plot and to describe the corresponding paths on the mountain. Exercise 3 also focuses on a point which is a saddle point of the altitude function. Students should be able to complete this discussion in a single class period with time at the end to summarize their results.