The distance from the point (2,2,2) is unbounded from above along the plane z=x+1. There is a minimum but not a maximum. Here are the contour curves:
Plot3D[x + 1, {x, 0, 4}, {y, 0, 4},
AxesLabel -> {x, y, z},
MeshFunctions -> {Norm[{#1 - 2, #2 - 2, #3 - 2}] & }]
