Module 13 :  Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 39 :  Constrained maxima / minima [Section 39.2]
39.2.3 Note( Lagrange's multiplier method):
 

In view of the above theorem, , to determine the absolute maximum/ minimum of a function subject to the constraint , we follow the following steps:

Step (i): Solve the equations

                                                            ---------(34)

Let

Step (ii): Let

Step (iii): Evaluate at each of the points in Find the largest of these values and the smallest of these values.

Step (iv): Ensure that and are the required absolute maximum and absolute minimum of respectively for the given constraints.

   
39.2.4 Examples:
(i)
 Let us find the maximum and the minimum of on the unit circle, that is, subject the the constraint
 

Since the conditions of the theorem 39.2.1 are satisfied, we consider the equations

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