SOLUTION: Find the dimensions that give the largest area for the rectangle. Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola y=8-x^2

Question 677470: Find the dimensions that give the largest area for the rectangle. Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola y=8-x^2
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the dimensions that give the largest area for the rectangle. Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola y=8-x^2
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It's symmetrical about the y-axis, so find the max area on the + side.
Area = x*y = x*(8-x^2) = 8x - x^3
dA/dx = 8 - 3x^2 = 0
x = sqrt(8/3) = 2sqrt(6)/3
--> y = 16/3
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Whole rectangle is 4sqrt(6)/3 by 16/3

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