Activity: Partial Derivatives from a Contour Map

Students are shown the contour graph of a function of two variables and asked to find the derivative. They discover that, without a function to differentiate, they must instead think of the derivative as a ratio of small changes. This requires them to pick two nearby points. Which two?

This is a graph of the function \(f(x,y)\):

  1. Find the derivative of this function.
  2. Find the derivative of this function at the leftmost of the indicated points.
  3. Find the partial derivative of this function at the leftmost of the indicated points with respect to \(x\).

Instructor's Guide

This activity is a set of SWBQ questions about finding a partial derivative from a contour graph. Show the contour graph and then ask, in an appropriate order depending on student responses:

  1. Find the derivative of this function.
  2. Find the derivative of this function at the leftmost of the indicated points.
  3. Find the partial derivative of this function at the leftmost of the indicated points with respect to \(x\).

Student Conversations

See the comments in the solution to the Student Handout.

Learning Outcomes