Question: Problem 7 : Let f ( x , y ) = 2 x + y . Then gradf = 2 vec ( i ) +

Problem 7: Let f(x,y)=2x+y. Then gradf=2vec(i)+vec(j), which is non-zero everywhere. Suppose that a fellow student of yours makes the following claim:
Student Claim: Since gradf0,f has no extrema on the unit disk D={(x,y)|x2+y21}.
Explain why this student is incorrect. What are the extreme values of f, and where are they located?
Problem 7 : Let f ( x , y ) = 2 x + y . Then

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