ve the following problems wit a). If the length of the diagonal o b). Find the maximum and minir the total length of its edges is

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 36E
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1. Solve the following problems with the second partial derivative test and with Lagrange's method.
a). If the length of the diagonal or a rectangular box has to be L, what is the maximum volume of the box?
b). Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm² and
the total length of its edges is 200 cm.
c). The plane x + y + 2z 2 intersects the paraboloid z = x² + y² in an ellipse. Find the points on the
ellipse that are closest and farthest from the origin.
=
Transcribed Image Text:1. Solve the following problems with the second partial derivative test and with Lagrange's method. a). If the length of the diagonal or a rectangular box has to be L, what is the maximum volume of the box? b). Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm² and the total length of its edges is 200 cm. c). The plane x + y + 2z 2 intersects the paraboloid z = x² + y² in an ellipse. Find the points on the ellipse that are closest and farthest from the origin. =
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