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Unformatted text preview: in the domain of D ± x ² . So, the critical point(s) will come from the zeros of the derivative function. Since A ³ 0 (it represents area), the only zeros of D ² ± X ² are x & ´ A . Only x & A lies in the interval we are interested in, so it is the only critical point for us. Looking at the derivative function, we see that it has positive values on the interval ± 0, A ² , and negative values on ± A , ² ² . So, D ± x ² decreases on ± 0, A ² and increases on ± A , ² ² , creating a local and global min. at x & A . This means that the rectangle of area A with the largest diagonal arises if the side lengths are x & A , and y & A x & A , i.e. it is a square....
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This note was uploaded on 03/24/2012 for the course MATHEMATIC 101 taught by Professor Many during the Spring '10 term at Sabancı University.
- Spring '10