Module 13 :  Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 39 :  Absolute maxima / minima [Section 39.1]
 

which is attained at the points as well as at , and

which is attained at as well as at .

(ii)
Let us find the triangle for which the product of the sines of the three angles is the largest. If we denote two
 

angles by and then the required function to be maximized is

It is obvious from the nature of the problem that the function will have absolute maximum. Note that

Thus, vanishes at each boundary point. At other points, i.e., for the equations are given by

Since

above equations give us

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