The critical points of the function f(x, y) = 5x² - 3xy + y² - 15x - y + 2 are determined by calculating the partial derivatives and setting them to zero. The partial derivatives are ∂f/∂x = 10x - 3y - 15 and ∂f/∂y = -3x + 2y - 1. Solving these equations simultaneously yields the critical point (3, 4). The classification of this critical point can be performed using the second derivative test.
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