Module 13 :  Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 39 :  Absolute maxima / minima [Section 39.1]
(3)

Show that the function

has only one critical point and that is a point of local maximum. Does function have absolute maximum at that point?
Answer
 
(4)
Find the dimensions of a rectangular box of maximum volume that can be inscribed inside a sphere of radius .
  Answer
 

 

(5)
Find the dimensions of a rectangular box of a given volume with minimum surface area.
  Answer
7