Stationarity gives xy²=−4 and x²y=2. Thus y=2/x² and x·4/x⁴=−4, so x³=−1: x=−1,y=2. The Hessian at this point is [[8,−8],[−8,2]], determinant 16−64=−48<0, so it is a saddle. There is exactly **1**.
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