Maximum/Minimum Problems (1 Viewer)

[RoXaH]

Fitz 15e)
Q6
A rectangular box whose base is a square is to be made so that its total surface area is constant. Prove that the volume of the box is greatest if the box is a cube.

 

[ozzievictor]

Area = A = 2L**2 + 4L*H where A = Constant

Solve for H in terms of L

H = (A-2L**2) / (4L)

Volume = V = L**2 H

Substitute for H in terms of L

Differentiate V with respect to L

Minimum at zero of dV/DL which occurs when A = 6L**2

Substitute back for H gives H = L

 

[Timothy.Siu]

lol its victor