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Differentiation 12

 

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發問:

A piece of wire of length of 60 cm is bent to form a rectangle. Find the maximun area of the rectangle.

最佳解答:

let x be the length of rectangle width of rectangle = (60-2x) / 2 = 30 - x the area A of rectangle = x(30 - x) = 30x - x^2 option A (by differentiation) dA/dx = A' = 30 - 2x differentiate dA/dx = A'' = -2 x = 15 the area A = 15(30-15) = 225 option B (by completing the square) the area A of rectangle = x(30 - x) = 30x - x^2 A = -(x^2 - 30x) A = -[(x^2 - 30x + 225) - 225] A = -(x-15)^2 + 225] as -(x-15)^2 is always
其他解答:0D7DAC4E7B8CAAC5

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