Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.7 Constraints and Lagrange Multipliers, #11 · Multivariable Calculus · Lagrange multipliers

Draw the hyperbola … touching the circle

Draw the hyperbola $x y = - 1$ touching the circle $g = x^{2} + y^{2} = 2$ .
The minimum of $f = x y$ on the circle is reached at the points
____. The equations $f_{x} = λ g_{x}$ and $f_{y} = λ g_{y}$ are
satisfied at those points with $λ =$ ____.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.7 Constraints and Lagrange Multipliers, #11

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