Question: (2 marks) Consider f(x, y, s, t) = (u, v) where u = x2+ 4x2st - 32 V = 2xy2 - 3s2 + yt -

(2 marks) Consider f(x, y, s, t) = (u, v) where u = x2+ 4x2st - 32 V = 2xy2 - 3s2 + yt - 4 (a) Using Implicit Function Theorem, prove that f (1, 1, 0, 2) = (0, 0) and there exists open sets U and V in R2 containing (1, 1) and (0, 2) respectively, a continuously differentiable function g : U -> V such that f(x, y, g(x, y)) = (0,0) for all (x, y) E U. as (b) Compute ay when (x, y, s, t) = (1, 1, 0, 2)

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