1. A rectangular box is placed in the first octant, with one corner at the origin and the three adjacent faces in the coordinate planes. The opposite point P(r, y, z) is constrained to lie on the paraboloid r2 + y? +z = 1. Which P gives the box of greatest volume? (a) Show that this problem leads to maximizing f(r, y, z) = ry – ry – ry*. (b) Find the critical point of f in the first octant. (c) Identity the nature of the critical point using the second derivative test and find the maximum of f in the first octant.
1. A rectangular box is placed in the first octant, with one corner at the origin and the three adjacent faces in the coordinate planes. The opposite point P(r, y, z) is constrained to lie on the paraboloid r2 + y? +z = 1. Which P gives the box of greatest volume? (a) Show that this problem leads to maximizing f(r, y, z) = ry – ry – ry*. (b) Find the critical point of f in the first octant. (c) Identity the nature of the critical point using the second derivative test and find the maximum of f in the first octant.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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