Module 4 : Local / Global Maximum / Minimum and  Curve Sketching
Lecture 11 : Absolute Maximum / Minimum [Section 11.1]
(ii)
 Let
 

We want to find absolute maxima and absolute minima of . Since

The critical points of in the given domain are and

Comparing the values of at we get absolute minima to be and absolute maxima to be

(iii)
A rectangular box, open at the top, is made from a metal sheet of 16cm x 30cm by cutting out four squares of
  equal size from the four corners and bending the sides. We want to find the size of the square so that the box has largest volume.
   
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