MediumLagrange multipliers

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.7 Constraints and Lagrange Multipliers, #17 · Multivariable Calculus · Lagrange multipliers

(d) Draw the pointed curve … to see why it is not…

These problems develop the theory of Lagrange multipliers.

(Example of failure) $λ = f_{y} / g_{y}$ breaks down if $g_{y} = 0$ at the minimum point.

(a) $g = x^{2} - y^{3} = 0$ does not allow negative $y$ because ______.

(b) When $g = 0$ the minimum of $f = x^{2} + y$ is at the point ______.

(c) At that point $f_{y} = λ g_{y}$ becomes ______ which is impossible.

(d) Draw the pointed curve $g = 0$ to see why it is not tangent to a level curve of $f$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.7 Constraints and Lagrange Multipliers, #17

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