Module 13 : Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 39 : Constrained maxima / minima [Section 39.2]
39.2
Constrained maxima/minima
In many practical problems, one has to find extreme values of a function whose domain is constrained to lie on a particular region in space. Let us look at some examples.
39.2.1
Examples:
(i)
Find the point closest to the origin on the plane .
Here we want to find in the plane such that the value
is the smallest.
(ii)
A space satellite in the shape of an ellipsoid enters earth's atmosphere and its
surface begins to heat. After an hour, the temperature at the point on the surface of the probe is
One would like to find the hottest point on the surface of the probe. That leads to the problem of finding absolute maximum for on the ellipsoid.
closest to the origin on the plane 
.
in the plane 
such that the value 
enters earth's atmosphere and its
on the surface of the probe is 
for 
on the ellipsoid. 
