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anonymous
 one year ago
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anonymous
 one year ago
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This Question is Closed

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2I change it to x, y instead of x1, x2 for convenience. \(f(x,y) = 3xyx^3y^3\), it is a symmetric function, hence \(f_x = 3y3x^2\\f_{xx}= 6x\\f_y= 3x3y^2\\f_{yy}= 6y\\f_{xy}=f_{yx}=3\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2The rule to figure out whether it is max or min: \(if~~f_{xx} <0, f_{yy}<0 ~~at~~(a,b)\rightarrow\) it is max \(if~~f_{xx}>0, f_{yy}>0~~at~~(a,b)\rightarrow\) it is min

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do I disregard the f_xy and f_yx?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2We will use it them if the conditions above doesn't fit.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and both f_xx and f_yy would be equal to zero only when x and y are equal to 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which would make f_x and f_y critical points, but I dont know if thyre a max or min because the second order derivative at those points isnt negative or positive

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2Oh, I am sorry, to find max/min, we use \(f_x=0,f_y=0\) not \(f_{xx}, f_{yy}\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2Tell me , what do you get for the point?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so for the points that make f_y equal to zero, did you get x=0 or 1^(1/3)?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2how? \(f_x= 3y3x^2=3(yx^2)=0\) iff \(yx^2=0\) \(f_y = 3x 3y^2= 3(xy^2)=0\) iff \(x y^2=0\) Hence we have \(y=x^2\\x=y^2\) only (0,0) and (1,1) are solutions for both them, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh i added something wrong. I see now. Thanks! but only (1,1) would be a solution correct? because it says in the problem that x1 and x2 (x and Y) are greater than .5

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2I don't know yet. I have to check one by one. Now (0,0) consider \(f_{xx}f_{yy}f^2_{xy}\) at (0,0) , what do you have?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2oh, ok, I forgot that condition. YOu are correct

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2now, check the same expression for (1,1)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait whats the f^2_xy?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2\(f_{xy}=3\rightarrow f_{xy}^2=9\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it just the squared value of f_xy? I apologize for all the questions but the first class was yesterday so im coming into this knowing nothing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What is the purpose of FxxFyyF^2xy?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2Yes, so it is >0, right? > (1,1) either max or min. Now, consider if it is max or min by :

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2\(f_{xx}\) at (1,1)= ? \(f_{yy}\) at (1,1) =?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0They're both negative meaning its a max

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2yyyyyyyyyyyyyyyyyyyyyyyyyyyes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait what was the FxxFyyFxy thing I havent seen that yet

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Was that just to determine the value of the point?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Where did the formula come from?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2we have fxxfyyf^2xy to find out the saddle point or max/min point if it is <0, the point is saddle point if it is >0 the point is either max or min.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Whats a Saddle point? again, sorry for all the questions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nevermind i got it. Thanks so much
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