# Math

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y equals= 12 minus x^2?

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1. If the rectangle has width 2x, then the area is

a = 2xy = 2x(12-x^2)
da/dx = 24 - 6x^2 = 6(4-x^2)
da/dx=0 when x=2
So, the largest area is 4(12-2^2) = 32

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