Let x and y be the sides of two squares such that y = x - x 2 . The rate of change of area of the second square with respect to the area of the first square is

Question

Let x and y be the sides of two squares such that y = x - x 2 . The rate of change of area of the second square with respect to the area of the first square is, 1 − 3 x + 2 x 2, 1 + 3 x − 2 x 2, 2 x, x + 2 x 3 − 3 x 2

MARKS App · Accepted Answer

Area of the first square is A 1 = x 2 . Area of the second square is A 2 = y 2 = x - x 2 2 = x 2 + x 4 - 2 x 3 So, the value d A 2 d A 1 = d A 2 d x d A 1 d x = 2 x + 4 x 3 - 6 x 2 2 x = 1 - 3 x + 2 x 2

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