Module 13 : Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 39 : Constrained maxima / minima [Section 39.2]
Thus, are the points on the surface closest to the origin.
39.2.7
Remark:
The method of Lagrange's multipliers extents when we have more than one constraint. Suppose we want to find extremum a function with constraints
where and have continuous partial derivatives in a neighborhood of These can be found by comparing the values of at points which satisfy the simultaneous equations
and for which
and
39.2.8
Example:
Let us analyze the problem of finding find the points on the intersection of the planes
that are closest to the origin. This is same as finding the minimum value of
are the points on the surface 
closest to the origin. 
with constraints 
and 
have continuous partial derivatives in a neighborhood of 
These can be found by comparing the values of 
at points which satisfy the simultaneous equations 
