A box (with no top) is to be constructed from a piece of cardboard with sides of length A and B by cutting out squares oflength h from the corners and folding up the sides.hAFind the value of h that maximizes the volume of the box if A = 19 and B = 23.(Use decimal notation. Give your answer to two decimal places.)h g

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Asked Nov 10, 2019
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A box (with no top) is to be constructed from a piece of cardboard with sides of length A and B by cutting out squares of
length h from the corners and folding up the sides.
h
A
Find the value of h that maximizes the volume of the box if A = 19 and B = 23.
(Use decimal notation. Give your answer to two decimal places.)
h g
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A box (with no top) is to be constructed from a piece of cardboard with sides of length A and B by cutting out squares of length h from the corners and folding up the sides. h A Find the value of h that maximizes the volume of the box if A = 19 and B = 23. (Use decimal notation. Give your answer to two decimal places.) h g

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Expert Answer

Step 1

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When squares of side h are cut at the corners of the cardboard, a box is obtained whose length is 23-2h, width is 19-2h and height is h The volume of the box becomes V (23-2h) (19-2h)h

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Step 2

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dV 0 dh d (23-2h)(19-2h)h]=0 dh d (437h-84h2+4h)=0 dh 437-168h 12h2 = 0

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Step 3

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437-168h12h2 0 -(-168) -168) -4(437)(12) 2(12) 168 4453 h = 24 42-453 42 453 h 6 6 Use Second derivative test and check at which value the maximum occurs d'v (437-168h+12h2) dh dh =-168 + 12h

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Math

Calculus

Derivative