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%2F105c1b83-7e99-453e-80b1-81643ac6bf98%2F6d9a281b-f6ae-401d-a6a8-01ea25e21897%2Fj89p6zo_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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