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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.6 Maxima, Minima, and Saddle Points, #28 · Multivariable Calculus · Gradient & optimization

Draw the triangle with corners at …, and

These problems minimize the Steiner distance $f = d_{1} + d_{2} + d_{3}$ and related functions. A computer is needed for 33 and.

Draw the triangle with corners at $(0, 0), (1, 1)$ , and $(1, - 1)$ . By symmetry the Steiner point will be on the $x$ axis. Write down the distances $d_{1}, d_{2}, d_{3}$ to $(x, 0)$ and find the $x$ that minimizes $d_{1} + d_{2} + d_{3}$ . Check the $12 0^{\circ}$ angles.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.6 Maxima, Minima, and Saddle Points, #28

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