Finding Level Curves of f(x,y)=xy

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In summary, the conversation discusses finding the level curves for a given function and the values of x that can be used. It is clarified that x can have any positive or negative value, but cannot be 0 as it would make the function undefined.
  • #1
ozgurakkas
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Question as follows

f(x,y)=xy , find the level curves for c= +-1,+-2,+-3,+-4,+-5

My first attempt was to set f(x,y)=c

c=xy and y=1/x C and this is an hyperbolic function. Is that right?

I am also confused what values x can get. I know it is restricted and x>0.
Can x get the same value as C ?
 
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  • #2
ozgurakkas said:
Question as follows

f(x,y)=xy , find the level curves for c= +-1,+-2,+-3,+-4,+-5

My first attempt was to set f(x,y)=c

c=xy and y=1/x C and this is an hyperbolic function. Is that right?

I am also confused what values x can get. I know it is restricted and x>0.
Can x get the same value as C ?
Why is it restricted to x> 0? Unless something else is said, y= C/x is only restricted to x not 0. Other than that, x can have any positive or negative value whatever C is.
 
  • #3
Question does not say it is restricted. I said it because x is in the denumerator. if it is 0 then it is undefined.
 
  • #4
Yes. But not being 0 does not mean it must be positive! x can be any positive or negative number.
 

What is the purpose of finding level curves of f(x,y)=xy?

The purpose of finding level curves of f(x,y)=xy is to visualize the behavior of the function on a two-dimensional plane. It allows us to see how the function changes as we move along different paths on the plane.

How do you find level curves of f(x,y)=xy?

To find level curves of f(x,y)=xy, we set the function equal to a constant value, usually represented by the letter c. Then, we solve for y in terms of x, which gives us an equation for a straight line. Repeating this process for different values of c will give us a family of parallel lines that represent the level curves of the function.

What do the level curves of f(x,y)=xy tell us about the function?

The level curves of f(x,y)=xy reveal the direction and magnitude of change of the function as we move along different paths on the plane. They also show us the regions where the function has constant values, allowing us to identify critical points and extrema.

What is the significance of the spacing between level curves of f(x,y)=xy?

The spacing between level curves of f(x,y)=xy represents the rate of change of the function. If the spacing is small, it indicates a steep change in the function, while a larger spacing suggests a more gradual change. In addition, the spacing can also reveal any symmetry or patterns in the function.

How can level curves of f(x,y)=xy be used in real-world applications?

Level curves of f(x,y)=xy can be used in various real-world applications, such as in economics, engineering, and physics. They can help in analyzing and understanding the behavior of variables and their relationships in a system. For example, in economics, level curves can be used to represent the demand and supply of a product, while in engineering, they can aid in optimizing designs and predicting performance.

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