[Math] How to sketch the level curves

multivariable-calculus

Let $f(x,y) = (x^2+y^2-1)(2x+y-1)$.

Then how can I sketch the level curves of $f(x,y)$?

Thank you for your help in advance.

Best Answer

According to the definition of level curves, if we are given a function of two variables $z=f(x, y)$,the cross-section between the surface and a horizontal plane is called a level curve or a contour curve. Thus, level curves have algebraic equations of the form: $$f(x, y) =k$$ for all possible values of $k$. Now let's do this goal by using a mathematical software like Mathematica or Maple. I did it by Maple 16 for you:

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