Chap11Sec6: Problem 9 Previous Problem List Next 2 points) Find the maximum rate

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Chap11Sec6: Problem 9 Previous Problem List Next 2 points) Find the maximum rate of change of f(,y)In( Maximum rate of change: + y')at the point (4.5) and the direction in which it occurs Direction (unit vector) in which it occus: Note: You can eam partial crecit on this problem. Preview My Answers Submit Answers You have attempted this problem O times You have 6 attempts remaining Email instructor Page genarated at 01/3/2018 at 1050am EST mew0K © 1996-2015 i renw mah4 Iww.ve son 2. tol pewie 2, some wenk K Po ct MacBook Pro 5 6 8 Ul

Explanation / Answer

f(x,y)=ln(x2+y2)

Gradient f(x,y)=<fx,fy>=<2x/(x2+y2),2y/(x2+y2)>

At point (4,5)

Gradient f(x,y)=<2*4/(42+52),2*5/(42+52)>=<8/41,10/41>

Therefore direction is (8/41,10/41)

And the maximum rate of change is

((8/41)2+(10/41)2)=(164)/41=2(41)/41

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