Question

Let S :={(x, y, z) ∈ R3 : x2+ y2 − z + 1 ≤ 0} . Let f : R3→ R be defined by f(x, y, z) := x + y + z .

Find the extrema for f restricted to S. Are these extrema global? Justify your answer.

[ Hint: S = S◦ ∪ ∂S with S◦ :={(x, y, z) ∈ R3: x2 + y2 − z + 1 < 0 and ∂S :={ (x, y, z) ∈ R3: x2 + y2 − z + 1 = 0 ]

Answer 1

Answer:

yes

Step-by-step explanation:

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