Find and classify the critical points of the following function: ...

[ETearle]

Question 1

A rectangular box with no top has given surface area  S.  Find the length, width, and height of the box if the volume is as large as possible.
◦ length = width = ,  height =  
◦ length = width = ,  height =  
◦ length = width = ,  height =  
◦ length = width = ,  height =  
◦ length = width = ,  height =  

Question 2

Find and classify the critical points of the following function: f(x, y) = (y- 2x)⁵ + 30x³ - 15y³.
◦ saddle points are (0, 0), (, - ) and (- , ), maximum at (3, -3) and minimum at (-3, 3)
◦ saddle points are (0, 0), (, - ) and (- , ), minimum at (3, 3) and maximum at (-3, -3)
◦ saddle points are (, - ) and (- , ), maximum at (3, 3) and minimum at (-3, -3)
◦ saddle points are (0, 0), (, - ) and (- , ), maximum at (3, 3) and minimum at (-3, -3)
◦ saddle points are (0, 0), (, - ),  (- , ),  (3, 3), and  (-3, -3)

[smrerig]

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[ETearle]

TYSM

[cpetit11]

Gracias!