11/18/2023 0 Comments Ap calc optimization problems![]() The two equations above are the constraints. The base length of the rectangle is b = 2 x (a distance of x on the left and the right side). Our objective is to maximize the area of the rectangle.īecause the parabola touches the rectangle at its upper corners, we know that the height of the rectangle is the same as the y-coordinate of the upper right corner point. Solutionįirst, let’s sketch the graph of the parabola as well as a typical inscribed rectangle. Example: Rectangles and Parabolasįind the largest area possible for a rectangle inscribed between the parabola y = 9 – x 2 and the x-axis, with its base on the x-axis. The hardest thing about optimization problems is the setup (Steps 1-2), because that changes from problem to problem. You might have to find the values of the other variables or quantities now.
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