The gradient of the function f (x, y, z) = √x +√y + √z is
and the tangent plane at the point (x0 , y0 , z0 ) is
What are the intercepts? To find the x-intercept, we set y = z = 0 and obtain x = √c √x0 . Similarly, the y-intercept is y = √c √y0 and the z-intercept is z = √c √z0 . Their sum is
because the point (x0 , y0 , z0 ) satisfies f (x0 , y0 , z0 ) = √c. Thus the sum of the intercepts of any tangent plane does not depend on the point, where the tangent plane is computed
