Maxima and minima of two variables
Multivariable and vector calculus · Mathematics
Study notes
Q: Find and classify the critical points of f(x,y) = x^2 + y^2 - 2x - 4y + 1. fx = 2x - 2 = 0 gives x = 1. fy = 2y - 4 = 0 gives y = 2. Critical point: (1,2). fxx = 2, fyy = 2, fxy = 0. D = (2)(2) - 0 = 4 > 0, fxx > 0. Local minimum at (1,2), value f = 1 + 4 - 2 - 8 + 1 = -4.