Rectangle and Parabola
Find the dimensions of a rectangle of maximum area, whose base lies on the x axis, and whose upper vertices lie on the parabola y = 12 - x^2. And what is the maximum area?
posted by Zaux at
9:25 PM
3 Comments:
32
Let (x,y) be the coordinates of the top right corner of the rectangle.
Are of rectangle = 2xy = 2x(12 - x²)
A = 24x - 2x³
dA/dx = 24 - 6x² = 0 => x = 2
So Amax = 48 - 16 = 32
Chris,
32 it is
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