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a9 - University of Toronto at Scarborough Department of...

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University of Toronto at Scarborough Department of Computer & Mathematical Sciences MATA33 Assignment 9 Winter 2008 Quiz 9 on this assignment will be written in the 11th tutorial, which takes place during the week of March 31 - April 3. There is no quiz during the 10th tutorial (the week of March 24 - 28). See the Notes at the bottom of this assignment for further details. Study: Section 17.7. Read ahead in Sections 17.8 and 17.10. We omit Section 17.9 Problems: 1. Section 17.7, Pages 776 - 777 # 1 - 3, 6 - 8, 10 - 12, 16, 18 - 20, 23, 24, 29, 33, 34. 2. A delivery company accepts only rectangular boxes who length plus ”girth” do not sum over 108 cm (The ”girth” of a rectangular box is the perimeter of a cross-section. Search ”girth” in Wikipedia). Find the dimensions of an acceptable box of largest volume. 3. In this question let f ( x, y ) = x 2 - y 2 - 2 x + 4 y + 6 (a) Use the critical point concepts and the second derivative test (i.e. Rules 1 and 2, pages 770 - 772) to find out that f has a critical point at (1 , 2) but no relative extrema there.
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