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Point) Find the point(s on the cone51" 2y" that are closest = the point3,0).The point(s_Hint: If f > 0 then V f is minimized exaclly when f is minimize...

Question

Point) Find the point(s on the cone51" 2y" that are closest = the point3,0).The point(s_Hint: If f > 0 then V f is minimized exaclly when f is minimizedIf you dont get Inis Exams!tries, VOJ can see similar example online) . However, try t0 use this a5 ast resor 0r aiter YOu nave already solved the problem_ There are no See Similar Examples on the

point) Find the point(s on the cone 51" 2y" that are closest = the point 3,0). The point(s_ Hint: If f > 0 then V f is minimized exaclly when f is minimized If you dont get Inis Exams! tries, VOJ can see similar example online) . However, try t0 use this a5 ast resor 0r aiter YOu nave already solved the problem_ There are no See Similar Examples on the



Answers

Find the points on the cone $z^{2}=x^{2}+y^{2}$ that are closest
to the point $(4,2,0) .$

Hi. Mhm. We're given here. The words of a closed convex polygons. Within the physical region of the functions are 541. What is R5 from a one next vortex. Three comma five. Next vortex or geometry? Next to our text to come a pipe. You wanna check here that maximally the function at eight X plus nine wives. Where it gets maximized for the objective functions which are for five from 1. This will become 14 Plus nine by this. 49. Next 3- five. This will become 24 plus 45. That is coming out to be 69. Next we have more common tree That's coming out of it 32 Plus 27. That's coming up to be 59. Next we have 2:05. That is human has 16 plus 45. That is giving us 16 months. The maximal is coming out to be 60 nine here and which is the option 69 option too. Thank you.

Okay, So for this problem, tried to minimize the function. If because thio x minus one square plus why minus two square plus a Z square with constraint equation G equals two x squared plus y square minus the square equals to zero. So use LeBron multiplied method. The greedy interfaith equals to two X minus two toe y minus four in a to Z and the Gregan of G equals to two x two y minus two c eso we have a system of equations. Uh huh uh, two X minus two equals 22 times Slam dykes to y minus four equals to two times Lambda y to Z equals two minus two Lambda Z. So we start with the last equation here. That means we have two different cases. So the first cases Z equals zero. But if C equals zero, we go back to this constraint equation. G x y Z equals to zero in this X squared plus y squared equals zero. And this equation gives us X equals toe. Why equal to zero? But this result will violate the first two equations. So this is not a solution in our in this problem that means we have to consider another case that will be loved A close to minus one. So if Lambda Acosta Biden swan if Lambda equals toe minus one, we are able Toe Express. Uh, were you able to solve X and y so X equals to one has why close toe one now, once we solve this x and y Mhm. Mhm. Yeah. Once we solve this exit while we go back to the constraint equation people, it gives us the equals two plus miners fruit off five over to. So we have two different points. P one equals to one half one Ruutel five over to two equals to one half one minus Ruutel five over to. But, uh, the day off F at this two point other. Same so f equals toe one or four plus one plus 544 which is total reform. So the distance, uh, to the 0.11120 The minimum distance to the point will be Rudolph F, which is Rudolph 10. Divide by two. So this is a million point, and it happens with P with the point is p Y o p. Two

For you in the function here, ethical five explodes three. Right here we have the the corners of the polygon, the physical region. We have to depend on the maximum value. The function here 24 00. The long term maximum value, export three comma zero. Pretty good material. We will have 15 Next 3:01 values 13 plus three at his 18 next one comma three. Value is five For the 29 that is body next is. Yeah. Obama too values being outside of class. Thanks. Let us take serving house. Make some of this coming out to be 1818. Thank you.

The problem is finding the point on the corn. The squire is you go to X square plus y square that a closes stitches a point or two zero first. Well, I need point X Y c on the corn If we're not the as the distance between X y Z and or two zero have B square, it's a cultural X minus or squire us Why minus two square See story. And if we replace this square by X square, plus y square he squared is equal to X minus four square. That's why months too Squire US exploiter us. Why squad here with you know that this function as half acts Why, then we compute partial half tracks. This is a caught you two times x minus for us two ax. This is a photo for six months, right? I shall ask. Partial y is equal to human terms y minus two As to why this is a cultural or why minus four selling this to your questions. A fax Because zero y zero we have the function of facts. Why has only one critical point go to two and why I could want face the function affects y has only one critical point. Then we know affects why hi global minimal while you on the point to one because intuitively there must be a point on secure plane that is contest into the point four to zero the saints affects warehouse has only one critical point. It must be, in fact, why must have them minimal while you respond. In this case, we have. They squired is equal to five half three years ago to pass on minus until foul. This two points are the points on the corn. That is that our proudest to the point sworn to zero.


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