Consider a continuous function f : B₁ (0) → R with B₁ (0) CR². The function is C¹ on the interior of its domain, namely B₁ (0), but the function has no critical points. Also consider the function g: [0,2] → R2 with g(t) = (cost, sint) Select all statements that must be TRUE. f has no local maximum. Of has no global maximum. f has a saddle point. fog has a global maximum. fog has a local maximum.
Consider a continuous function f : B₁ (0) → R with B₁ (0) CR². The function is C¹ on the interior of its domain, namely B₁ (0), but the function has no critical points. Also consider the function g: [0,2] → R2 with g(t) = (cost, sint) Select all statements that must be TRUE. f has no local maximum. Of has no global maximum. f has a saddle point. fog has a global maximum. fog has a local maximum.
Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
Section: Chapter Questions
Problem 1CE
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![Consider a continuous function f : B₁ (0) → R with B₁ (0) CR². The function is C¹ on the interior of its domain, namely B₁ (0), but the function has no critical
points.
Also consider the function g: [0,2] → R2 with g(t) = (cost, sint)
Select all statements that must be TRUE.
f has no local maximum.
Of has no global maximum.
f has a saddle point.
fog has a global maximum.
fog has a local maximum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71339e46-2ee5-403f-84a7-6d5a8d64b9c6%2F60f1b7a3-3d65-4419-bfa4-b0a33e354b94%2Fa8ae97n9_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a continuous function f : B₁ (0) → R with B₁ (0) CR². The function is C¹ on the interior of its domain, namely B₁ (0), but the function has no critical
points.
Also consider the function g: [0,2] → R2 with g(t) = (cost, sint)
Select all statements that must be TRUE.
f has no local maximum.
Of has no global maximum.
f has a saddle point.
fog has a global maximum.
fog has a local maximum.
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