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XSThe graph below shows y for x 2 0. Find the coordinates of the 9 + x2 maximum point:...

Question

XSThe graph below shows y for x 2 0. Find the coordinates of the 9 + x2 maximum point:

XS The graph below shows y for x 2 0. Find the coordinates of the 9 + x2 maximum point:



Answers

The function $f(x, y)=2 x+3 y+9-x^{2}-x y-y^{2}$ has a maximum at some point $(x, y) .$ Find the values of $x$ and $y$ where this maximum occurs.

Okay, let's go ahead and complete squares. So we are negative. Nine X square. Plus, it's so the first thing that we're gonna do he's kicked that negative nine out from the them eight square last fix. So we're gonna have X square miners eggs over nine because I want to take that nine from both of them. And this is putting forth. So the next thing is gonna be to observe the number that goes with the eggs. We have won over nine. We're gonna take that number, you're gonna divided right, too. So we were gonna have 18 now, and we're gonna square it, and we are gonna have it there, and we're going to subtract the same number. But since these he's multiply by negative nine where we are adding and subtracting east that number square and then my multiply by Negative. Now. Now, these one, we can't live in the cities and we can make this expression off. This number better is one over 36. And now these He's the square that we were trying to complete. And these eggs miners one over 18. It's quiet now. We have our birthdays. Then, uh um won over 18. Coma, one over 36 and scene in from off the square. We have negative nine. That is negative. That means that we have in the birthday cakes. Um, Max. C'mon. Okay, so we have a maximum, uh, won over 18 coma, one over 36. And if we observed the graph, it going sites with the number that we got, it looks like it very, very close to zero, because these two numbers are very small.

Why Eagled your X squared minus six. Thanks. Last night and the question I asked you commit in the square. Esquire is finding them. We knew my maximum on the function we call that literally can read. That s a X square minus Jude times three times x does three square And it's exactly the special formula for the ice cream. Honest, you be blessed. Be square Initial result in the I minus B totally square. So therefore we should get ICO Jew the X minus three square and just will be to commit in the square on this on campus. So far, we have a tax Iko Jude 30 And this one will be, uh, a minimum. ERM function here equal to zero.

The MX function is because toe two divided by nine times X plus 11 Holy square Here we're having award parabola vortexes Negative off 11 coma zero. So you get your 11 commas Little it is not white. It is on X X is so negative off 11 Let's it is negative 11 comma zero when it is aboard parabola. So here off this parable, always the medium Hallelujah At this point at vortex, so V is point off minimal and and mix mignon value It is the y value zero.

FX. It's four times off X minus six. Holy square. Negative off night. So here it is. Aboard parabola up, ward Parabola vortex. We have this six and minus night. So as it is, afford parabola and vortexes. Six comma, minus nine. So we can see here maximum value. This vortexes point off medium as it is, lowest point. So if we have to find the value maximum minimal tomainian value of this function is this is negative off night.


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