Level curves The two main ways to visualize functions of two variables is via graphs and level curves Both were introduced in an earlier learning module Level curves for a function z = f ( x, y) D ⊆ R 2 → R the level curve of value c is the curve C in D ⊆ R 2 on which f C = c Notice the critical difference between a level curve CLevel curves Scroll down to the bottom to view the interactive graph A level curve of \(f(x,y)\) is a curve on the domain that satisfies \(f(x,y) = k\) It can be viewed as the intersection of the surface \(z = f(x,y)\) and the horizontal plane \(z = k\) projected onto the domain The following diagrams shows how the level curves \f(x,y) = \dfrac{1}{\sqrt{1x^2y^2}} = k\ changes as \(kIe the level curves of a function are simply the traces of that function in various planes z = a, projected onto the xy plane The example shown below is the surface Examine the level curves of the function Sliding the slider will vary a from a = 1 to a = 1
Applet Gradient And Directional Derivative On A Mountain Shown As Level Curves Math Insight
