Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.7 Constraints and Lagrange Multipliers, #12 · Multivariable Calculus · Lagrange multipliers

Find the maximum of … on the circle … by solving …

Find the maximum of $f = x y$ on the circle $g = x^{2} + y^{2} = 2$ by
solving $f_{x} = λ g_{x}$ and $f_{y} = λ g_{y}$ and substituting $x$ and $y$ into $f$ .
Draw the level curve $f = f_{m a x}$ that touches the circle.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.7 Constraints and Lagrange Multipliers, #12

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