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.
Level_curve_graph.JPG

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.
Level_curve_graph.JPG