Find an equation of the tangent plane to the surface fx y z

Find an equation of the tangent plane to the surface f(x, y, z) = 7 at the point (1, 4, 5). Do not transform it - do not open parentheses.

Solution

Solution:

Let F(x,y,z) define a surface that is differentiable at a point (x₀,y₀,z₀) the equation of the tangent plane is

       Grad F(x₀,y₀,z₀) ^. < x - x₀ , y - y₀ , z - z₀ > = 0

Here f(x,y,z)=7, Grad f(x,y,z)=0, since it is constant function.

Hence there is no tangent plane to the given surface.