A level curve of a function f(x,y) is the curve of points (x,y) where f(x,y) is some constant value A level curve is simply a cross section of the graph of z=f(x,y) taken at a constant value, say z=c A function has many level curves, as one obtains a different level curve for Level curves will help you reduce a dimension by treating the function value as a constant That is, the level curves (more correctly "level surfaces") for for f (x,y,z)= 4x^2 y^2 9z^2 will be the three dimensionl graphs 4x^2 y^2 9z^2= C for different values of C Those will be a number of ellipsoids, of different sizes, one inside the otherIe 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
Session 25 Level Curves And Contour Plots Part A Functions Of Two Variables Tangent Approximation And Optimization 2 Partial Derivatives Multivariable Calculus Mathematics Mit Opencourseware
