use logarithmic differentiation to find dy/dx y= ((x+2)sqrt(1-x^2))/4x^3

If

then taking the logarithm of both sides and expanding the right side gives

Differentiate both sides with respect to x :

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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