Asked by Anonymous
The figure below shows the curves y=square root of x, x=9, y=0 and a rectangle with the sides parallel to the axes and its left end at x=a. Find the dimensions of the rectangle having the maximum possible area.
Answers
Answered by
Steve
If the lower left corner is at x, the height is sqrt(x) and the width is (9-x)
a = 9x^1/2 - x^3/2
a' = 9/(2x^1/2) - 3/2 x^1/2
= 3/(2x^1/2) * (3 - x)
a' = 0 at x=3
a(3) = sqrt(3) * (9-3) = 6sqrt(3)
a = 9x^1/2 - x^3/2
a' = 9/(2x^1/2) - 3/2 x^1/2
= 3/(2x^1/2) * (3 - x)
a' = 0 at x=3
a(3) = sqrt(3) * (9-3) = 6sqrt(3)
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