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.

Understanding Business
12th Edition
ISBN:9781259929434
Author:William Nickels
Publisher:William Nickels
Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
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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.
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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