1. Consider the following function: f(x) = x² + 8x cos y – 2x + 10 cos y – 8 cos" y +8 cos y, x = (x, y) E R². Using the necessary and sufficient conditions, compute by hand all minima and maxima of...

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Extracted text: 1. Consider the following function: f(x) = x² + 8x cos y – 2x + 10 cos y – 8 cos" y +8 cos y, x = (x, y) E R². Using the necessary and sufficient conditions, compute by hand all minima and maxima of f(x). Classify these minima and maxima. Hint: To classify the minima and maxima, use the identity a² + 8xz – 2x + 10z – 822 + 823 = 2z(2z – 3)² + (x + 4z – 1)² – 1.