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Find the relative maximum and minimum valuesflxy)-x+yz _ 2x - 10ySelect the correct choice below and if necessary; fill in the answer boxes to complete your choice_...

Question

Find the relative maximum and minimum valuesflxy)-x+yz _ 2x - 10ySelect the correct choice below and if necessary; fill in the answer boxes to complete your choice_The function has relative maximum value of f(xy) = at (xy) = (Simplify your answers_ Type exact answers. Type an ordered Pair _ in the second answer box:) The function has no relative maximum valueSelect the correct choice below and, ifnecessary; fill in the answer boxes complete your choiceOA. The function has relative minimum value

Find the relative maximum and minimum values flxy)-x+yz _ 2x - 10y Select the correct choice below and if necessary; fill in the answer boxes to complete your choice_ The function has relative maximum value of f(xy) = at (xy) = (Simplify your answers_ Type exact answers. Type an ordered Pair _ in the second answer box:) The function has no relative maximum value Select the correct choice below and, ifnecessary; fill in the answer boxes complete your choice OA. The function has relative minimum value of flx,y) = at (XY)= (Simplify your answers_ Type exact answers. Type an ordered pair in the second answer box ) 0 B. The function has no relative minimum value_



Answers

Find the relative maximum and minimum values. $$f(x, y)=x^{2}-y^{2}$$

Stop about question nine. We need to find that relative extreme hours in this case. So let's differentiate this with respect to experts. So we have FX as trading, whereas a conference. So we have two experts to likewise we have f y as do I minus four. We equate affixed to zero. So we have two X plus two equated to zero. This means that excess minus one on we have a four equated to zero, so we have to buy minus 40 This means that wires toe eso we have one critical point which is minus one and two. Let's find out f x x now. So fxx is pretty simple. It is just too every y y is also to on f x y zero because zero because in effect there is no why so d would be two times two is four for minus zero square zero. So we have four since India's positive and f x X is also positive. It means that we have a relative minima act minus one and two because this is the critical point on the value of the relative minimum would be one plus four minus two minus eight for my students to focus on the streets, reminded traitors minus five. So this is the value. They're a little minimum, and this is the point where the little minima occurs.

Talk about questions. Seven. So, in order to find a little extreme a well, first differentiate with respect awakes. So we have two weeks minus two. Then we differentiate with respect to why? Which is two y score. He quit this 20 So we have two weeks minus two is equal to zero. This means that we have access one. And if we quit a fight to zero, we have to wipe us four a zero. The speeds that wires minus two. So we just have one critical point, just one on minus two on board Now we'll fine f x x f x y and f Y Y f x x would just be too f x y would be zero because in effect, there is no why and why. Why will also be so we have d S f x x times x y, which is four minus requires where which is just 20 So since these already positive on FXX is also positive, So we have a relative minima a t one and minus two, and that relative minimum would be with place except by one and by by minus two. So we have one purse for this will be minus two. This will be minus eight and minus two. So we have five minus two is 33 minutes to is one What? Minus eight has minus seven. So this is the relative minimum, and this is the point where we have a relative minimum.

Question number one. We need to find a little Maxima and minima off this particular function So forceful. Differentiate with respect to X. Let's noted by f and with a subscript exit means that we're differentiating with respect to X treating while the constant so FX will be different station of X squares to x x y will just to be. Why? Because why is a constant on a wire square zero and off? Negative wires also zero. So we have two x plus y as the terrible, terrible respective eggs like where is the deliberate, the derivative? With respect, Why would be zero? Creating X is a constant This this would be excess would be to buy. This would be minus one, so we have X plus two by minus one. Now, what we do is really equate FX +20 and f y +20 to get, uh, critical numbers. So we have fxe zero. This means that two x plus y zero This means that why is negative two works? It's called Equation one, while for F from every we have X plus two by minus one, this is equated to zero. We already have the value of y as negative toe works or replacing Why bynegative to work. We have negative three Xs one, it needs the excess negative one or three. If X is negative one or three, then why would be negative two times x from this equation? So that will be to over three. So a point off interest would be negative. One or three and two or three. Uh, while now we need to verify with others, has a maximum rate of animals. So that's where F double dash F X X comes in derivative find, uh, derivatives again with respect to work. So that will just be too. Then we find out why. Why? So we decorate this, uh, regrettable. This with respect to y will just be too on. Then we get we find x y So ex wife from here will just be one. Now we find me which is f x six times f y y minus f x y square. It comes out as four minus one, which is three. So since the d is positive on F X X is also greater than zero. It means that we have ah, relative minimum. This implies that we have the relative minimum at the critical point. Let's rewrite this little minima at minus one or three on to over three. And the value off F X Y at this point would be minus one or three whole square. But ex wife. So we have X. Why? Plus why? Square minus y. So this is 119 minus 2/9 plus four or nine minus 2/3. So this comes out as, uh, 3/9, minus two or three, which is nothing but minus from one or three. So this is the relative minimum. While this is the point where we have the relative

Let's talk about Question three s in order to find a little maximum minimum force will differentiate this with respect. Works keeping y as a constant. So we have two by minus three years a square, and then we'll do the same thing. Keeping fixes a constant So we have to hire, uh, minus Dubai over here once again. Actually, it will be two X because X is taken as a conference. The differentiation of why, with prospective violence just one. So we have two x managed to weigh. Now we're here. We quit affects 20 So we have two y minus three extra square is nothing but zero. So from here, we have to Wire is as three. It's a square scholar equation one and like ways. From here we have two x minus tree Where square zero. The value off why from this equation is nothing but three x square or two. So this is equal to zero. If you simplify this, we have four X minus nine. X square is equal to zero. This means that exist. Taken out, we have four minus nine x as equal to zero on this one correction Here This is actually to wise. So we have to rewrite this way mystically Go three Why we're here. So let's rewrite this. As we have two weeks minus two y is equal to zero. So from here we'll place the value off two wires. Three X squared is equal to zero. Access taken out. We have two minus three x 0 to 0. This means that either x zero or two minus three x zero to ministry 80 than from here We have three Xs Stewart me start access to over three s So we have two values off extra. Me I we have values of X from here on the corresponding values of why would be effects zero on two y zero, which means that y zero if X is to over three onto A s three times for over nine. It means that why else on we simplify this, we again get two or three. So there are two points off interest. 1001 is two or three to over to you. All right, let's find out whether this has a little maximum minimum or or neither. So if you find fxx f x X is nothing but the derivative off FX respect the works again, which is nothing but minus six x. You find out why Why f y y is again the derivative with respect. Why? Which is nothing but minus two on we find f x y, which is the relative of FX with respect. So why so with respect to why and features to be to Then we find f we find d which is f x x times f y y minus effects while square. So this consult as elects minus four. Uh, Now, if you place our first value in which x zero then d is actually minus four. So whenever D is less than zero, there is no, uh, minimum or maximum So we cannot really take it on if access to over three then we're just interested in the science. Over three minutes it would be 12 minus four, which is eight. So it since D is positive it will have a rid of Maxima or MINIMA. And we also see that if access to over three have, xx will be negative. It means that we have a relative since f x X at this point would be negative So we have Ah, relative Maxima. And that relative maximum value would be FX that effects FX common. Why would be with taste the values of X and wires. So we have two times. Ex wife, both hard. Global tree minus two will treat you with nothing but a photo. 8/27 minus. Here we have for over nine. So this comes orders 8/9 minus 8/27 minus 4/9. Took common denominator. 27 we have 24 minus eight minus. Uh, yeah, this will be, uh, 12. So we have to inform. Minister is 12 and 12. Minus eight is four. So we have four or 27. So this is the value of the relative Maxima wild. This is the point where the relative maximum occurs.


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