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I have the following queston:

Consider the function $f(x,y)=(4-x^2-y^2)^2$.

a) Sketch all the level curves for $f(x,y)=c $ for $c=0$, $c=4$ and $c=25$

b) Also plot the level set for $f(x,y)=16$.

So, I know to find the level curves I have to solve the equation equal to my value of c. However, I have tried looking online but I can't understand what the difference between a level curve and a level set is. I would naturally just solve it in the same way as a level curve with $c=16$. But the distinction between a level curve and a level set is made so I believe there must be some difference in approach, but I personally cannot see what it is.

Any insight would be appreciated.

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1 Answer

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A level curve is a type of level set. For $c=16$, the only point in the solution set is the origin, $x=y=0$. A single point is not a curve.

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