Grades 11-12 Video Solutions 2010-11&12 Video Solutions 2010 problem24

11&12 Video Solutions 2010 problem24

Video Transcription

Video Summary

The problem involves optimizing the expression \(x^3 + y^3\) for non-negative real numbers \(x\) and \(y\) such that \(x + y = 2\). By substituting \(y = 2 - x\) and analyzing the function over \(x\), critical points and endpoints can be identified to find extreme values. At \(x = 0\), \(y = 2\), resulting in the maximum value \(8\). At the critical point \(x = 1\), \(y = 1\), yielding the minimum value \(2\). Thus, the difference between the maximum and minimum values is \(6\), corresponding to choice B.

Keywords

optimization

expression

critical points

extreme values

non-negative