Module 13 :  Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 39 :  Constrained maxima / minima [Section 39.2]
 

with constraints,

The equations to be solved are

Substituting the values of from the first three in the last two equations gives

This gives

That this is the required point, can be justified as in the previous example.

   
  Practice Exercises
(1) The temperature at a point in -space is given by Find the highest
  temperature on the unit sphere
 

Answer
(2) Find the point nearest to the origin on the surface defined by the equation
  Answer
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