1. Suppose y is inversely proportional to x and the constant of proportionality

Question

1. Suppose y is inversely proportional to x and the constant of proportionality equals 6 . What is the minimum of the sum of x and y if x and y are both positive? 2.Find the area of the largest rectangle with one corner at the origin, the opposite corner in the first quadrant on the graph of the line f(x)=40-5x , and sides parallel to the axes. The area= ?

Explanation / Answer

Inverse proportion ---> y = k/x Here, k = 6, so y = 6/x Minimize the sum S = x + y But, y = 6/x, so substitute: S = x + (6/x) S'(x) = 1 - (6/x^2) = 0 (6/x^2) = 1 x^2 = 6 x = sqrt(6) y =sqrt(6) S = 2sqrt(6)

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