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Real World Activity Now that we have worked with partial derivatives and their applications, this activity will focus on using partial derivatives as a tool
Real World Activity
Now that we have worked with partial derivatives and their applications, this activity will focus on using partial derivatives as a tool to predict and interact with the world around you.
- First, find a location outside somewhere that is not flat (i.e., a hill, street, or something else that is curved and sloped).
- Take a picture of this location, and if you are able, try to use editing software to indicate the precise point in your picture where you will be doing this activity.
- Next, use a ruler, yardstick, or other device to try and approximate the change in height in two directions. Pick a direction to call x and estimate the change in the elevation z for an increase of one foot in x. Then, in a direction that is 90 degrees counterclockwise representing y, do the same thing.
- Explain the significance of the two values you determined, and then use them to find an approximate equation of a tangent plane at this point (you may assume your starting point is the origin for convenience).
- Finally, say that you were going to walk in the <1,1>-direction; would your path be initially ascending, descending, or stay at the same elevation? Use your previous answers to explain your reasoning.
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