Question 1034416: Find the dimension and area of the rectangle with the greatest area that can be implemented in a semi-circle with radius 3 m. Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website! I will give only an answer in which one side of the rectangle is along the diameter of the semi-circle. This way the center actually cuts the said side into two parts of equal length. Let one-half of the side have length x meters, and the height y cm. Hence, , or
The area is then given by A = 2xy, or .
Get the derivative of A wrt x and set to 0:
<==> ==> , or .
If , then A' > 0.
If , then A' < 0.
==> there is local max at .
Incidentally, the maximizing dimensions are , and the maximum area is .
