Observe that the tangent hyperparaboloid PB depends on the same number of variables as the function f, i.e. on 3 variables. Therefore, the tangent hyperparaboloid to a function of three variables cannot be visualized directly; it lies in 4-space.

However, we can slice the tangent hyperparaboloid along the x-, y- and z-axes. If each point (x,y,z,f(x,y,z)) has a tangent hyperparaboloid then slicing the surface together with the tangent hyperparaboloid at a given point yields three paraboids that are tangent to the respective slice surface of the hypersurface.