Figure 2: Graph of g(x, y) = x2 + y2. When we considered functions and graphs of one variable, one of the first things we did was to transform those graphs through shifts and stretches. We can do the same thing with functions of two variables. Figure The function f(x,y) = x 2 + y 2 + 2x + 8y has a relative minimum (at the bottom of the valley). It is often important to locate the relative maximum or the relative minimum of a function, just as for a function of 1 variable it is common to seek the relative maximum or relative minimum. Section Functions of Several Variables. The level curves of the function z=f (x,y) are two dimensional curves we get by setting z=k, where k is any number. So the equations of the level curves are f (x,y)=k. Note that sometimes the equation will be in the form f (x,y,z)=0 and in these cases the equations of the level curves are f (x,y,k)=0.

# Multiple variable functions f x y

Calculus 3 Lecture 13.1: Intro to Multivariable Functions (Domain, Sketching, Level Curves), time: 1:49:07

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