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?
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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.
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: