Math CentralQuandaries & Queries


Question from Jay, a student:

Determine the area of the largest rectangle that can be inscribed between the x-axis and the curve defined by y = 26 - x^2.

Hi Jay,

I inscribed a rectangle as you described. I let the x-coordinate where the rectangle touches the parabola be x and then the y-coordinate is 26 - x2.

rectangle inscribed

The area of the rectangle is A(x) = x × 2(26 - x2). Use the calculus you know to maximize A(x).


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