Module 13 : Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 39 : Constrained maxima / minima [Section 39.2]
i.e.,
It is easy to check that the points that satisfy these equations are
Since the unit circle is closed and bounded and is continuous on it, attains its absolute maximum/minimum on it, and are the largest/smallest of the values
that satisfy these equations are 
is continuous on it, 
attains its absolute maximum/minimum on it, and are the largest/smallest of the values 
has absolute maximum 
, absolute minimum 
. 
