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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.6 Maxima, Minima, and Saddle Points, #27 · Multivariable Calculus · Gradient & optimization

Problems 28–42 minimize the Steiner distance … **and related functions

Choose $c > 0$ so that $f = x^{2} + x y + c y^{2}$ has a saddle point at $(0, 0)$ . Note that $f > 0$ on the lines $x = 0$ and $y = 0$ and $y = x$ and $y = - x$ , so checking four directions does not confirm a minimum.

Problems 28–42 minimize the Steiner distance $f = d_{1} + d_{2} + d_{3}$ and related functions. A computer is needed for 33 and 36–39.

This exercise builds on another exercise in its source book, which isn't shown here.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.6 Maxima, Minima, and Saddle Points, #27

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**Problems 28–42 minimize the Steiner distance** … **and related functions

Problems 28–42 minimize the Steiner distance … **and related functions