Question: lagrange multipliers smooth function f : R3 - R is said to be harmonic if its Laplacian Af = fxx + fyy + fzz is

lagrange multipliers

smooth function f : R3 - R is said to be harmonic if its Laplacian Af = fxx + fyy + fzz is identically zero. Consider the smooth function f : R3 -> R given by f (x, y, z) = 22+ 242 -322. (a) Show that f is harmonic, i.e., fxx + fyy + fzz = 0. (b) Let K = {(x, y, z) : 32 + y" + 2"

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