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Calculus & Optimisation - Largest Area of a Rectangle Inscribed by a Parabola
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This video provides an example of how to find the rectangle with a maximum area bounded by the x-axis and a quadratic function.
Learn how to find the largest area of a rectangle that can be inscribed inside a semicircle, given that the semicircle has radius r. Since this is an optimization problem, draw a picture of the problem and write what you know. Then identify optimization and constraint equations. Solve the constraint equation for one of the variables, and plug the solution into the optimization equation to get the optimization equation in terms of one variable. Then take the derivative of the optimization equation, set it equal to zero, and solve for the variable. Make sure to answer the question you were asked!
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Learn how to find the largest area of a rectangle that can be inscribed inside a semicircle, given that the semicircle has radius r. Since this is an optimization problem, draw a picture of the problem and write what you know. Then identify optimization and constraint equations. Solve the constraint equation for one of the variables, and plug the solution into the optimization equation to get the optimization equation in terms of one variable. Then take the derivative of the optimization equation, set it equal to zero, and solve for the variable. Make sure to answer the question you were asked!
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