
 31.html 
  The point(s) where the gradient of the Lagrangian vanishes (i.e., is equal to 0) are points where the least and greatest distances must occur, if they do occur. 
  Although we have not proven so directly, it is safe to conclude that (1,1,0) and (1,1,0) are the points on the hyperboloid that are closest to the origin. 
  A sphere of radius 1 centered at (3,4,0) is subjected to a gravitational potential field whose source is a point mass located at the origin. 
 faculty.etsu.edu /knisleyj/multicalc/Chap3/Chap31/315.html (358 words) 
