Lagrange multipliers, using tangency to solve constrained optimization

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/lagrange-multipliers-and-constrained-optimization/v/lagrange-multipliers-using-tangency-to-solve-constrained-optimization The Lagrange multiplier technique is how we take advantage of the observation made in the last video, that the solution to a constrained optimization problem occurs when the contour lines of the function being maximized are tangent to the constraint curve.