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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: ... Learn how to find maximum values with constraints using This video introduces a really intuitive way to solve a constrained optimization problem using We analyze the behavior of the "shifted" quadratic form f(x,y)=x^2+2x+y^2+2y over the closed disk of radius 2 centered at the ... Calculus 3 Lecture 13.9: Constrained Optimization with f(x,y) = 0.5x^2 + 0.5*y^2 a constraint S: g(x,y) = 0.5x^2 + y^2 = 1 (ellipse) as the constraint is closed and bounded, f S must attain ...

We address the problem of finding the maximum and minimum value of a function subject to a constraint. The method of

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Last Updated: May 22, 2026

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