Student handout: 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?

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 with respect to \(x\) at the leftmost of the indicated points.

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