Level Curves
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Example 1:
Question:
Find the level curves of heights C = -1, 0, 1 for f(x,y) = x+y+1
Solution:
- For height C = -1 ( Yellow Line )
- f(x,y) = x+y+1 = -1
- x+y+1 = -1
- y = -2-x
- slope = -1
- y-intercept = -2
- For height C = 0 ( Blue Line )
- x+y+1 = 0
- y = -1-x
- For height C = 1 ( Red Line )
- x+y+1 = 1
- y = -x
This is the graph that refers to Example 1.
Example 2:
Question:
Find the level curves of heights C = 4, 1, 0, and -1 for f(x,y) =
Solution:
- For height C = 4 ( Blue Circle )
- For height C = 1 ( Red Circle )
- For height C = 0 ( Yellow Dot )
- Only solution is x = 0, y = 0.
- For height C = -1
- Does not exist because has to be greater than equal to 0.
This is the graph that refers to Example 2.
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