Please show the complete clear solution and rules that are used in every steps, Thank you so much! 1. A long metal sheet with a width of L meters is formed into a gutter by bending up two ofits sides so that the cross-section of the gutter is an isosceles trapezoid. Find themaximum volume of the gutter.2. Find and classify all the critical points of f (x, y) = 7x – 8y + 2xy – x² + y³.3. Find the moving trihedral and the curvature at any point of R(t) = (In(6t), e1-t,5t).

Given: 2.Let us consider the given curve equation, fx,y=7x-8y+2xy-x2+y3 -----1

Answered: 2. Find and classify all the critical…

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2. Find and classify all the critical points of f (x, y) = 7x – 8y + 2xy – x² + y³. %3D (1

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

Section9.4: Polyhedrons And Spheres

Problem 48E: Sketch the solid that results when the given circle of radius length 1 unit is revolved about the...

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Question

Please show the complete clear solution and rules that are used in every steps, Thank you so much!

1. A long metal sheet with a width of L meters is formed into a gutter by bending up two of
its sides so that the cross-section of the gutter is an isosceles trapezoid. Find the
maximum volume of the gutter.
2. Find and classify all the critical points of f (x, y) = 7x – 8y + 2xy – x² + y³.
3. Find the moving trihedral and the curvature at any point of R(t) = (In(6t), e1-t,5t).

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