6. Let the function $f: \mathbb{R}^3 \to \mathbb{R}$ be defined by $f(x, y, z) = 2x^2y + yz + \cos(z)$. Find all stationary points of $f$. Determine if any of them are global maxima or minima.
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The gradient of f is given by the vector (∂f/∂x, ∂f/∂y, ∂f/∂z). Taking the partial derivatives of f with respect to x, y, and z, we get: ∂f/∂x = 4xy ∂f/∂y = 2x² + z ∂f/∂z = y - sin(z) Setting these partial derivatives equal to zero, we have: 4xy = 0 2x² + z = Show more…
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