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DFTA5rclajivc extrema and sadole poings of tha functionSccdnt JctAAneria ~aPplicable (Ilantnsntt Cocnce erst enter DNE;TY)relatiy minimumTtn Matm]Y.2)Onillc >-va...

Question

DFTA5rclajivc extrema and sadole poings of tha functionSccdnt JctAAneria ~aPplicable (Ilantnsntt Cocnce erst enter DNE;TY)relatiy minimumTtn Matm]Y.2)Onillc >-valuet6,72){unratervnlsucJlt point6.y#

DFTA5 rclajivc extrema and sadole poings of tha function Sccdnt JctA Aneria ~aPplicable (Ilantnsntt Cocnce erst enter DNE; TY) relatiy minimum Ttn Matm] Y.2) Onillc >-valuet 6,72) {unratervnl sucJlt point 6.y#



Answers

Use Lagrange multipliers to find the maximum and
minimum values of the function subject to the given constraint.
$$
f(x, y, z)=x^{2}+y^{2}+z^{2} ; \quad x+y+z=12
$$

Are you going here? The given closeness for the corporal. Prolix Bless way. My just proves it so at a Jesus, I hate this car. Plus by square press six clip. So they path because do well our night a flirt and the ability because do we do eggs come up with a composite that have sequence lab ankle Touch it so that it was Goodbye, Rex, which is a good one, by the way, It is a part of my nurse. True by it was it so order Bigger thing exit quartile. Oh, what? There is a quarto. My rescue away on the X is a good Why does it? But it was square plus lies. God bless that square equals four. So do let's quit this life then plus minus two square. Because for bigot my advice Square requests here. Why? Because yes, my life, Rudy were it by three. Oh, well, I use a little bless O minus. No, but the and existing color too. Cool way, which is a goto plus or minus four by three. And that is a photo my just threw away, which is a total plus or minus for three. So you want to be grew by three. Come on for by three. I don't want my toes for your butt and people, because minus two by three Good mom, My last four by three Come on for by three Full function at the point people, because we do provide three. Bless for by three. My just do it do might have fought by they That is a good look. 16 by day at the point P two equals what we do. Why not? Still, But they let us for by day minus two, Windows four by three because my No. 16 there were but

Hello, You are here. Did you? In function is perfect because three express six right plus does the doctor constraint to live Skype plus full way square. Plus the square equals 40 So we can do like their life because land up there touching that is 36 Because I do Forex, comma aid way comma Boozer So we'll get lap equals three by for X but you think or do thanks Bye Pay play, which is incredible tool by does it for the gun friend Inclusion is do it square plus full of square. Plus they're square equals 40. So which would be like they did by my right square equals 40 Do that like well, I scored because 40 fired by love it Well, I goto plus on my last group 40 for they were But I love it since Texas in court of lie and excessive guilt away. And as that is a little four by three way the that point B weirdness rebuff Fortified by 11 coma fruit off fortified by 11 Call Mama, but three fruit fortified by 11. So you too sick or too why that's route fortified by 11 come up minus soup fortified by 11 hold up minus four by three. Moot fortified by 11. So Big F max If they got a three express excited press tools that Viterbi by using Point do you want so we'll get, like identified in the root find by 11. Have made it up, maybe uptake by the 60 point people, which will be minor stratified by a route find by 11.

Using the ground multipliers, we get the derivative with respect to X y z. You call it slammed. Uh, Times two x The dreaded with respect to why XY equals Lambda Times four. Why and the derivative with respect to Z X y equals Lambda Time 60. Now, if we multiply the first equation by X on both sides on the second equation by why on both sides on the 30 waging by Z on both sides, you'll notice that we get X y Z on the left side of all three equations so we can set the right hand side equal to each other. And so we get, um, the Times two X squared equals named attempts for y Squared equals Lambda time six. Z squared. And now if we divide each of these by chul and uh, will be left with X squared equals two y squared equals three z squared. And if you look at the constraint equation, you actually noticed that each of these x y and Z terms match up. And so, substituting into the constraint equation, we can write X squared plus X squared plus X squared equals six. And so we get three X squared equals six. Four X squared equals two, which gives X equals plus or minus Ruutu. Now we can just use this X equals plus or minus root, too to solve for y and Z via these equations. And so we get two equals two y squared, which of course, gives why it goes plus or minus one. And we get two equals three z squared, which gives us Z equals plus or minus route to over route three. So what we have is one point, which is where all three coordinates are positive. And if we evaluate that in the function half, we're going to get two over route three and for example, if we evaluate the same points, But where X is negative, we get a negative to over Route three. And so this value here is going to be our max. This value here is going to be our men, and the maxes will occur where zero for two of X y z our pot are negative and the men's are going to occur where one or three of X y z are negative.

Later on. Today we're going to solve a problem. Number 16 here. We have to minimize if, which is equals. X Square minus eight x That's my square minus 12 plus 48. Subject to X plus y minus eight equals zero. Capital of exp i Love Nike was X squared minus eight ticks plus my square minus two away plus 14 minus lambda and do X plus y minus eight f with respect to access two X minus eight minus lambda equals zero If it respected ways two y minus 12 minus lambda equals zero. If with respect to Love Dies X plus y minus eight equals zero. Well, because express toe x plus y minus eight equals zero and has a solution. X y that because three comma fight three x way equals three. Come out fighting. Thank you.


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