Question: Suppose the function f(x, y, z)=2x - 3y + z - 20 gives the temperature, in degrees Fahrenheit, at a point (x, y, z).
(a) Describe the isothermal surfaces of f.
(b) Calculate and interpret fz(0, 0, 0).
(c) If you are standing at the point (0, 0, 0), in what direction should you move to increase your temperature the fastest?
(d) Is f(x, y) = -2x + 3y + 17 an isothermal surface of f? If so, what is the temperature on this isotherm?