What is the largest possible area of a rectangle inscribed in the region bounded by the parabola y = x? and the line y = 4, where one side of the rectangle lies on the line y = 4 and two vertices of the rectangle are on the parabola y picture below)? = x2 (see one of the possible inscribed rectangle in the 4 Y = x²

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.