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The Gold Mine

Keywords: Multivariable Calculus, Partial Derivatives, Linear Approximation, Surfaces

mvgoldmine.jpg

Highlights of the activity

  1. This small group activity using surfaces is designed to provide a geometric description of linear approximation using the tangent plane.
  2. Students work in small groups to extrapolate information about the local density of gold to estimate the density elsewhere.
  3. The whole class wrap-up discussion emphasizes the geometric role of the tangent plane as an approximation to the surface, and the relationship of both to first- and second-order partial derivatives.

Reasons to spend class time on the activity

Useful visual application of partial derivatives to linear approximation.

Reflections

Instructor's Guide

Student Handouts

mvgoldminehand.pdf


Authors: (c) Aaron Wangberg and the "Raising Calculus to the Surface" team; used by permission.
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