![]() The partial derivative of f(x, y) with respect to x, ∂f/∂x, is what you get when you differentiate while interpreting y as a constant rather than a variable. Now we need to show why! Partial derivativesįrom your parenthetical comment, it appears that you may not have learned about partial derivatives but what you have done is perfectly valid. Then I input x = 2y to f(x, y) = y 2 – 4y + 3 = (y – 2) 2 – 1Īpparently this student has not done multivariable calculus, but has invented some of its basic concepts, particularly partial derivatives. ![]() (I’m not sure if I can make it to f(x) while it is actually f(x, y).) This is the first time I met this question, and here is my way:įirst I made f'(x) = 2x – 4y = 0. Find the value of x and y when f(x, y) is minimum. The question came from Kurisada a couple months ago:į(x, y) = x 2 – 4xy + 5y 2 – 4y + 3 has a min value. A recent question from a student working beyond what he has learned led to an interesting discussion of alternative methods for solving a minimization problem, both with and without calculus.
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