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Calculus:Derivatives


You are designing a rectangular poster to contain 50 inches squared of printing with a 4 inch margin at the top and bottom; and a 2 inch margin at each side. What overall dimensions will minimize the amount of paper used?

Verified Answer :

Lunaarchaic

(x − 8)(y − 4) = 50, so y = 4 + 50
x−8
. Then
A(x) = x

4 + 50
x − 8 
x > 8.
A
0
(x) = 4 −
400
(x − 8)2
, so A
0
(x) = 0 gives x = 18.
 A
00(x) = 800
(x − 8)3
> 0

so the function is concave up, so x = 18 is the absolute minimum. When x = 18, y = 9.

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