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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.6 Maxima, Minima, and Saddle Points, #57 · Multivariable Calculus · Gradient & optimization

The value of … theorems and … exercises is … (maybe)

The value of $x$ theorems and $y$ exercises is $f = x^{2} y$ (maybe). The most that a student or author can deal with is $4 x + y = 12$ . Substitute $y = 12 - 4 x$ and maximize $f$ . Show that the line $4 x + y = 12$ is tangent to the level curve $x^{2} y = f_{m a x}$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.6 Maxima, Minima, and Saddle Points, #57

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