(a) Find the minimum and maximum values of the function f: \mathbb{R}^{2} \rightarrow \mathbb{R}, \quad f(x, y)=x-y subject to the constraint x^{4}+y^{4}=32 Also, at which points are these minimum and maximum values achieved? Dr Mistake wishes to find the maximum and minimum values of a(x, y) = x,subject to the constraint b(x, y) =x² – y? = 1. For this, Dr Mistake applies the method of Lagrange multipliers to solve the system \nabla a(x, y)=\lambda \nabla b(x, y), \quad b(x, y)=1 and correctly obtains the solutions (x, y, A) = ±(1,0, }) to this system. However,Dr Mistake then incorrectly concludes that the maximum and minimum values of a(x, y) are ±1 and are achieved at (x, y) = ±(1,0). What did Dr Mistake do wrong? Explain Dr Mistake's mistake.

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