Question

Using Lagrange multipliers, find the dimensions and volume of the largest rectangular box in the first...

Using Lagrange multipliers, find the dimensions and volume of the largest rectangular box in the first octant with 3 faces in the coordinate planes, one vertex at the origin and an opposite vertex on the paraboloid z = 1 - x2 - y2.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant...
Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the given plane. x + 3y + 4z = 9
Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant...
Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the given plane. x + 4y + 3z = 12
Use Lagrange multipliers to find the dimensions of the rectangular box of maximum volume, with faces...
Use Lagrange multipliers to find the dimensions of the rectangular box of maximum volume, with faces parallel on the coordinate planes, that can be inscribed in the first octant of the ellipsoid 4x^2 + y^2 +4z^2=192
A rectangular box is placed in the "octant" x,y,z is less than or equal to 0,...
A rectangular box is placed in the "octant" x,y,z is less than or equal to 0, with one corner at the origin, the three adjacent faces in the coordinate planes, and the opposite point constrained to lie on the paraboloid: 10x + y2 + z2 = 1 Maximize the volume of the box.
Use Lagrange multipliers to find the volume of the largest rectangular box with edges parallel to...
Use Lagrange multipliers to find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid. 9x^2 + 9y^2 + 4z^2 = 324
Apply Lagrange multipliers to solve the problem. Find the dimensions of the box with a volume...
Apply Lagrange multipliers to solve the problem. Find the dimensions of the box with a volume of 8 ?3 that has minimal surface area.
Find the dimensions of the rectangular solid of largest volume which can be inscribed in the...
Find the dimensions of the rectangular solid of largest volume which can be inscribed in the ellipsoid x2/16+y2/4+z2/9=1 Hint: Let (?, ?, ?) represent one of the eight vertices of the solid. Then by symmetry the volume of the solid is ? = (2?)(2?)(2?).
Determine the dimensions of a rectangular box without lid, of maximum volume if the total surface...
Determine the dimensions of a rectangular box without lid, of maximum volume if the total surface is fixed at 64 cm2 . Solve without using Lagrange multipliers.
Find the volume of the largest rectangular box with edges parallel to the axes that can...
Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid x^2/9+y^2/36+z^2/1=1 Hint: By symmetry, you can restrict your attention to the first octant (where x,y,z≥0), and assume your volume has the form V=8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume:
1) Use calculus to find the volume of the solid pyramid in the first octant that...
1) Use calculus to find the volume of the solid pyramid in the first octant that is below the planes x/ 3 + z/ 2 = 1 and y /5 + z /2 = 1. Include a sketch of the pyramid. 2)Find three positive numbers whose sum is 12, and whose sum of squares is as small as possible, (a) using Lagrange multipliers (b )using critical numbers and the second derivative test.