Question
1. Let S be a level set surface of a C' function f : R" → R.
(la) Prove if p ES is an interior point of S then Vf(p)=0.
(1b) Conclude that the interior of the unit sphere S"-1 centred at the origin in R" is empty.
(Revised 2020-11-16)
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1. Let S be a level set surface of a C' function f : R" → R. (la) Prove if p ES is an interior point of S then Vf(p)=0. (1b) Conclude that the interior of the unit sphere S"-1 centred at the origin in R" is empty. (Revised 2020-11-16)

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