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Can anyone help with the question below? Any help is greatly appreciated. Use Lagrange multipliers to find the maximum and minimum values of the function

Can anyone help with the question below? Any help is greatly appreciated.

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)

f(x₁, x₂, ..., x_n) = x₁ + x₂ + ... + x_nx₁² + x₂² + ... + x_n² = 64

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