Let S be a closed n-cube with v(S) > 0 and suppose f : S –→ R is continuous on S (relative to S). (a) Prove that infs ƒ and sups f both exist, and that infs f < „IS Js f < sups f. v(S) (b) Prove that there exists xo E S such that f(xo) v(S)
Let S be a closed n-cube with v(S) > 0 and suppose f : S –→ R is continuous on S (relative to S). (a) Prove that infs ƒ and sups f both exist, and that infs f < „IS Js f < sups f. v(S) (b) Prove that there exists xo E S such that f(xo) v(S)
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![Let S be a closed n-cube with v(S) > 0 and suppose f : S → R is continuous on S (relative
to S).
(a)
Prove that infs f and sups f both exist, and that infs f < „S) Js f < sups f.
v(S)
(Ъ)
Prove that there exists xo E S such that f(xo) = „S) Js f.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1db0a8d-7a0a-4a06-9757-d3194d74bf23%2F5bfdca29-8b9b-463b-981f-1f2b98050641%2Fvn4j9t28_processed.png&w=3840&q=75)
Transcribed Image Text:Let S be a closed n-cube with v(S) > 0 and suppose f : S → R is continuous on S (relative
to S).
(a)
Prove that infs f and sups f both exist, and that infs f < „S) Js f < sups f.
v(S)
(Ъ)
Prove that there exists xo E S such that f(xo) = „S) Js f.
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