Quadratic functions long question?
2014-10-11 5:50 am
A homebuilder wants to build a deck on the back of a house. One side of the deck will share a wall with the house, and the other three sides will have a wooden railing. If the builder has enough wood for 15 meters of railing, what is the area of the largest deck he could build?
回答 (1)
2014-10-11 7:46 am
2W + L = 15
L = 15 - 2W
WL = A
W(15-2W) = A
A = -2W^2 + 15W; maximize A
dA = -4W + 15; A is maximized when dA = 0
-4W + 15 = 0
4W = 15
W = 15 / 4 = 3.75 m
L = 15 - 2W
L = 15 - 2(3.75) = 7.5 m
A = 3.75 * 7.5 = 28.125 m^2
L = 15 - 2W
WL = A
W(15-2W) = A
A = -2W^2 + 15W; maximize A
dA = -4W + 15; A is maximized when dA = 0
-4W + 15 = 0
4W = 15
W = 15 / 4 = 3.75 m
L = 15 - 2W
L = 15 - 2(3.75) = 7.5 m
A = 3.75 * 7.5 = 28.125 m^2
收錄日期: 2021-04-15 16:48:06
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