Question: We can graph a function f(x) of one variable as a curve in two dimensions, y=f(x). We can graph a function f(x,y) of two variables

We can graph a function f(x) of one variable as a curve in two dimensions, y=f(x). We can graph a function f(x,y) of two variables as a surface in three dimensions, z=f(x,y). It's more difficult to graph a function f(x,y,z) of three variables! One way to think about such a function is that it gives the temperature at each point (x,y,z) in space. A good way to visualize the function is to draw its level surfaces, the surfaces of the form f(x,y,z)=c.The temperature of a candle flame is about 1500F. The temperature of a typical room is 70F. Sketch a couple of representative level surfaces around the candle flame, which are surfaces for which all points on the surface have the same temperature, and label the temperature of each.

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