Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.6 Maxima, Minima, and Saddle Points, #51 · Multivariable Calculus · Gradient & optimization

(b)

Find lines along which $f (x, y)$ is constant (these functions have $f_{xx} f_{y y} = f_{x y}^{2}$ or $a c = b^{2}$ ):

(a) $f = x^{2} - 4 x y + 4 y^{2}$

(b) $f = e^{x} e^{y}$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.6 Maxima, Minima, and Saddle Points, #51

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