What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 3 − x^2?
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Okay here is the answer
Area = x * y
We need to find our X, because the height is a function of X.
You can divide this problem into 2 rectangles, each one to both sides of the y axis, and the "big" rectangle will be the sum of both.
so, the rectangle will have area = x * (12 - x^2)
you have to maximize it, so we differentiate it:
d(area)/dx = 12-3*x^2 = 0.
then x = 2
the area would be 2*(12-4) = 16
lets see if its maximum or minimum... if we choose x = 0, we would get a height o 12, but an area of 0, so its a maximum (without doing any derivative tests :D )
So the area of both rectangles would be 32 units squared
._. that wasn't even my problem. where did you get those numbers from