Attaining a maximum

Task number: 3172

The function \(f\colon \space \mathbb R^2 \to \mathbb R\) is defined as \[f(x, y) = \frac{1}{x^2 + y^2 + (x\cos(y) - 2x - 3e^y)^2 + 2}.\]

Prove that \(f\) attains its maximum value on \(\mathbb R\).

    Difficulty level: Easy task (using definitions and simple reasoning)
    Proving or derivation task
    Cs translation
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