Small White Board Question: Partial Derivatives from a Contour Map
None 2023
In this sequence of small whiteboard questions, 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?
- assignment_ind Small White Board Question 10 min. Student handout (PDF)
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This ingredient is used in the following sequences
1. << Electric Field of a Line Source From Potential | Gradient Sequence |
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Media
This is a graph of the function \(f(x,y)\):
- Find the derivative of this function.
- Find the derivative of this function at the leftmost of the indicated points.
- Find the partial derivative of this function with respect to \(x\) at the leftmost of the indicated points.
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:
- Find the derivative of this function.
- Find the derivative of this function at the leftmost of the indicated points.
- 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.- Keywords
- Learning Outcomes
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