Surface shading on an triangle Let's assume that in a triangle we have computed the brightness on the vertices of a triangle and we have found that it is maximum. 

Can any other point which lies on that triangle have more brightness than the maximum brightness on those vertices ?
That completely depends on how you are computing the shading. If you are then just linearly interpolating the shaded colours across the triangle, i.e. Gouraud shading then, clearly, the answer is "no".

However, if you are doing per-pixel shading by, say, interpolating normals and light directions, then you can easily get a brighter area away from the vertices.