Maximum integral Consider the plane x + 3y + z = 6 over the rectangle R with vertices at (0, 0), (a, 0), (0, b), and (a, b), where the vertex (a, b) lies on the line where the plane intersects the xy-plane (so a + 3b = 6). Find the point (a, b) for which the volume of the solid between the plane and R is a maximum.

Maximum integral Consider the plane x + 3y + z = 6 over the rectangle R with vertices at (0, 0), (a, 0), (0, b), and (a, b), where the vertex (a, b) lies on the line where the plane intersects the xy-plane (so a + 3b = 6). Find the point (a, b) for which the volume of the solid between the plane and R is a maximum.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 43E: A frustum of a cone is the portion of the cone bounded between the circular base and a plane...

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