13  Derivatives in many variables

If \(f = f(x,y)\) has a local maximum or minimum at \((x_0,y_0)\), then \(f_x(x_0,y_0) = 0\) and \(f_y(x_0,y_0) = 0\).

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Stewart, James, Daniel K. Clegg, and Saleem Watson. 2020. Calculus: Early Transcendentals. 9th ed. Cengage Learning.