Sketch level sets

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Homework Statement



I am very uncomfortable with the concept of "level sets" and don't quite get what it means.

Homework Equations



y = 2(x1)^2 - (x1)(x2) + 2(x2)^2


y = 2x1^(1/2) * x2^(1/2)

The Attempt at a Solution



I'm not even sure where to start... Can anyone please give me some basic knowledge of how to approach these problems?
 

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Ray Vickson
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Homework Statement



I am very uncomfortable with the concept of "level sets" and don't quite get what it means.

Homework Equations



y = 2(x1)^2 - (x1)(x2) + 2(x2)^2


y = 2x1^(1/2) * x2^(1/2)

The Attempt at a Solution



I'm not even sure where to start... Can anyone please give me some basic knowledge of how to approach these problems?
A level set of f(x1,x2) is the curve f(x1,x2) = constant. If z = f(x1,x2) describes a hill or mountain, a level set of f would be a path of constant elevation. That's all!
 
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A level set of f(x1,x2) is the curve f(x1,x2) = constant. If z = f(x1,x2) describes a hill or mountain, a level set of f would be a path of constant elevation. That's all!
Thanks...

So in the top example above,

2(x1)^2 - (x1)(x2) + 2(x2)^2 = C?

What I'm confused about also is how I would graph it...
 
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Ray Vickson
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Thanks...

So in the top example above,

2(x1)^2 - (x1)(x2) + 2(x2)^2 = C?

What I'm confused about also is how I would graph it...
For a given numerical value of C, the equation describes some type of curve; you need to figure out what that curve is, and draw it. Surely you must have done problems like that in the past!
 
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For a given numerical value of C, the equation describes some type of curve; you need to figure out what that curve is, and draw it. Surely you must have done problems like that in the past!
Thanks... The only thing I don't get is figuring out what the curve is when there is always two xs, i.e. y = ((x1)^(2))*((x2)^(2))... Do you use algebra to put it into a form you can understand better?

Sorry for the newb questions...
 

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