Can anyone explain why number 1 is true HONOR PLEDGE: I certify that I have exam

Question

Can anyone explain why number 1 is true HONOR PLEDGE: I certify that I have examination, nor do I have reason to believe that anyone else has. neither given nor received unauthorized aid on this Date l01 Signature: Part I. True or False (30 points: 6 points for each of the following 5 problems) Determine whether the following statement is true or false. Please circle your answers. 1. Every continuous function f (a, y must attain an absolute minimum and absolute maxi mum value on 4r2 +9y2-1. ru lse 2. If z = f(x(s), y(s, t)), then Di-by 2. Ifz=f(z(s),y(s,t)), then az=df5y . and fw(1,2) = 5, then f has a local 3.. If (1,2)=0-1, fez(1, 2) -2, fey(1,2)-3 minimum at (1,2) True

Explanation / Answer

TRUE :every continous functionf(x,y) must attain absolute minimum and absolute maximum value on 4x2+9y2=1

4x2+9y2=1 is a closed bounded region(ellipse) in R2

according to extreme value theorem if f is continous on closed ,bounded region in R2,then f attains a absolute minimum and absolute maximum value on D

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