5

Points]DETAILSSCALC8 14.7.020.Find the local maximum and minimum values and saddle point(s_ separated list. If an answer does not exist; enter DNE:) f(x, sin(x) sin...

Question

Points]DETAILSSCALC8 14.7.020.Find the local maximum and minimum values and saddle point(s_ separated list. If an answer does not exist; enter DNE:) f(x, sin(x) sin(y) , FT<* <t VMT#y<tlocal maximum value(s)local minimum value(s)saddle point(s)(x,ylAHl

Points] DETAILS SCALC8 14.7.020. Find the local maximum and minimum values and saddle point(s_ separated list. If an answer does not exist; enter DNE:) f(x, sin(x) sin(y) , FT<* <t VMT#y<t local maximum value(s) local minimum value(s) saddle point(s) (x,ylAHl



Answers

Find all the local maxima, local minima, and saddle points of the functions. $$f(x, y)=y \sin x$$

In this question were given the function I have X y ico to one off x plus x y because one of the why and the first time we need to find the first specially with u F X, They were getting into one of the X Square. Yeah, that's why he coaches zero. So from here, it means that why ICO to one other X square and similarly, the f why we go to, uh, minus one, otherwise square and with the nicotine. So therefore we have the X. We go to one otherwise square. So we're going to use this choir here, put into this guy, then we should get thanks we go to Nah thanks. Our fallen now and then we have doesn't even only if the X minus expel for e coaches zero So conflict the X outside on. Then we have one minus Expo three e coach is zero. Therefore, we have XY coaches zero Mexico to one when x which is also why we go to under fight. So we'll be, uh, it will be notified in this case here and then we're not considered this one, so no value. Yeah, and I went actually 21 while you were equal with you one. And therefore, we have only one value off the critical point here. So we have only one. And the second step, we need to find a second brush on the river to f X x. Then we get Nico June, uh, to off Explore three now and then F y why we go thio over. Why about three on f x y we go to one Therefore add the on 11 Do we ghenda have x x times f y y on the f x y square they will record you now we will have the f x x would other 11 So I'm going to times that we have times two minus no one square So it doesn't include to the three credit and zero and f x X equal to two is created and Sarah Therefore we can conclude that we will have the loco minimum and ex uncle had upon 11 Yeah, yeah,

In this question was given the function I have x y you go to the able to x times the course I under wine and the first time we need to find the first passion the river to U F X. They were getting close to the 22 X tempts the course. I wonder why we wanted from equal to zero. And it only happens when the course I Why most coaches? Zero? Because I wanted to do even Only if the wine was ico Thio Uh I want to plus the and pie where the hand will be an integer here, Andi then the partially roof. To respect to the wine, we get equal to the B two X and then have minus side Why we sent an e coaches. Oh, doesn't even only if the no side why must equal to zero and isn't happens even only if the Y was equal to the en pie for and will be in the integer And then everyone we see that we only need the condition on the Y on and X will be free. Therefore, we have the critical point. We have everything money up them. So it could be a long about the expenses. So it will be, uh why will be on the form and pie. It will combine together here. So we should have, uh here. First of fun will be This one will be We cannot have both course inside at the same time will be equal to zero. Definitely critical point will be No, no critical pond here and then when we have no critical point, we don't need to go to the second steps. So that's what we done here. Different is no local extreme er and no set upon here.

In this problem, we are given the shown in equation and asked to find all of the local minimums, local maximums and settle points of the function. Now, in order to do this, we need to find all the critical points And to find the critical points we need to find the partial with respect to X and they partial with respect to why the person with respect to X is going to be two X, those two. Why we're gonna set that equal to zero on the pressure with respect of why is going to be two X and we're gonna set that equal to zero. As you can see, if you can solve the second equation for X and so that into the first equation and so they get, the X is equal to zero. So plugging that into the first equation, we get two. Why is equal to zero? And so why? It's actually also equal to zero, and we have found our one and only critical 10.0 comma zero now in order to find so that's a local minimum mocha maximum or saddle point. We need to find the pressure with respect to X twice that's going to be too partial with their sector. Why twice? Which is actually going to be zero in the A partial with respect to X and then with respect to why which we look at this equation for and that's going to be, too. And so when we play that into our expression for D, we get to a times zero minus two squared or zero minus four, which is negative for which is less than zero, which means that we have a subtle point at the point 00 and that is our answered.

Pants. Claire. So enumerate here. So we're given the function signed X ton sign why? And were given two domains. Native pie two new pie where X and negative pie to part for a while. So here I wrote down the first and second derivatives, and she substitute f X equals zero f y equals cereal. We got the condition. Co signed Time sign is equal to zero and sign x Times co signed. Why is equal to zero? So, using the critical point, we're gonna find those. So it's we've been negative. High half negative. By how negative By house. Sarah, we did have by half. Oh, yeah. Zero negative pie, huh? 00 So, hi. Uh, I have negative by how I have so and by half. And we have to find the second derivatives at the critical point. So for our 1st 1 you get, um as Double X is equal to negative one. And, um, there might not be enough space to write it down, so just write a job. This so it is gonna be in the order. No, Too much x y. Is this for So for our first point negative pie negative. You get negative. One zero and negative. One for a second point. Negative pie. Half zero. We get zero zero zero. My third point, You get 10 one. Our fourth point, we get 000 So on our fifth point, we also get 000 and our six point we also gets. We'll continue here for 1/7 point by half. Common Negative. How happy. At 101 for eight point gets a reserve zero. And for a final point, we get negative ones. We're gonna ply the second derivative test for each of the points. And for our first point, we got one which is bigger than zero. For a second point, we get zero for 1/3 point, we get one 00 zero one 01 So we know that negative. I have a comma negative by half and pie, Huh? My heart for minimum. Our maximum were negative by how I have the pie house. Negative. I have our minimum. And the less all right saddle


Similar Solved Questions

2 answers
9. Sketch the function and graph: Write the function in terms of functions in form f(l cuc(L) . Find the Laplace Translorm:0 <t <3 t _3 if 3 < t < 5 t -2 5 < t < 6 if 6 < t <8 4L il 8 < Lg(t)
9. Sketch the function and graph: Write the function in terms of functions in form f(l cuc(L) . Find the Laplace Translorm: 0 <t <3 t _3 if 3 < t < 5 t -2 5 < t < 6 if 6 < t <8 4L il 8 < L g(t)...
5 answers
1 Consider & batterylthat is sclecled t0 be 24VIlWhat would you expect (he Tesistance ofithe heating element belil the radiated powcr is to tota] 60W?9.6 n 1044Q 1244n 8.2 0A certain material has a total resislance of 2.64x 10-/nland resistivity mcasurcd atl9.71 * 10mlollm Youl cut thc malcrial with a cross scclion of 4202 mm,what is tie matenall s length?10.55 mm bil5 5 mm 032mm d. 32imm
1 Consider & batterylthat is sclecled t0 be 24VIlWhat would you expect (he Tesistance ofithe heating element belil the radiated powcr is to tota] 60W? 9.6 n 1044Q 1244n 8.2 0 A certain material has a total resislance of 2.64x 10-/nland resistivity mcasurcd atl9.71 * 10mlollm Youl cut thc malcria...
5 answers
Jon8.4 0 C17 5 5 5 into into into the out the Foutofthe page 0 page the the pagehe 1 'Moiaq6 cm and | 4.2The magentic ffield
Jon 8.4 0 C17 5 5 5 into into into the out the Foutofthe page 0 page the the page he 1 'Moiaq 6 cm and | 4.2 The magentic ffield...
2 answers
4. Find the product of two matrices. Indicate the type is the matrix C (Is it Hermitian , Skew-Hermitian. Or neither ?) Find det € and the eigenvalues of €.c=[71%[8 2
4. Find the product of two matrices. Indicate the type is the matrix C (Is it Hermitian , Skew-Hermitian. Or neither ?) Find det € and the eigenvalues of €. c=[71 %[8 2...
1 answers
Tion 6If the elements X,y and XY of a group G have order 2, then Xy#yX .{et eredSelect one: Truered out ofFalselag question
tion 6 If the elements X,y and XY of a group G have order 2, then Xy#yX . {et ered Select one: True red out of False lag question...
5 answers
(a) Graph the polar equationYnet Cuno qephTqualon conuelMunenTadud ccntciancquauonAcntthc €rc Mth nou:ana cente {J; 01Grman 0 Inc #0m Tulo DeconeiKoraalaincOateLne C0 4e eqyalon Decdic Delur rouOtapnChcic Wue ~ooLiJ CenictCanten Lne CcungnToau
(a) Graph the polar equation Ynet Cuno qeph Tqualon conuel Mu nen Tad ud ccntci an cquauon Acnt thc €rc Mth nou: ana cente {J; 01 Grman 0 Inc #0m Tulo Deconei Koraalainc Oate Lne C0 4e eqyalon Decdic Delur rou Otapn Chcic Wue ~ooLi J Cenict Canten Lne Ccungn Toau...
1 answers
Consicer tl following WatrixDx s the system Ai ( ht non-trivial solution? State the: runk and nullity of A.Dscrilmu: tlu slution sci WAr (j A5 vc(ui "quation AI Kive the geomettical iter- pretalion,Exptessing [o; wi a; ai], state which colunmns of A urc linenr independent And whuc h lineurly dependent_ W is the relationship between tl Columns o A"
Consicer tl following Watrix Dx s the system Ai ( ht non-trivial solution? State the: runk and nullity of A. Dscrilmu: tlu slution sci WAr (j A5 vc(ui "quation AI Kive the geomettical iter- pretalion, Exptessing [o; wi a; ai], state which colunmns of A urc linenr independent And whuc h lineurly...
5 answers
Compute the definite integrals. Use a graphing utility to confirm your answers.$int_{0}^{pi} x cos x d x$
Compute the definite integrals. Use a graphing utility to confirm your answers.$int_{0}^{pi} x cos x d x$...
5 answers
B) trans-]-isopropyl-4-ethylcyclohexaneDraw bond-line formula (use solid and dash wedges to show proper stereochemistry) and Fischer projection formula of (R)-6-bromo--hexen-3-ol. (1 point x 2 = 2 points)
b) trans-]-isopropyl-4-ethylcyclohexane Draw bond-line formula (use solid and dash wedges to show proper stereochemistry) and Fischer projection formula of (R)-6-bromo--hexen-3-ol. (1 point x 2 = 2 points)...
1 answers
Use the techniques from Section 9.4 and Section 9.5 to determine a fundamental matrix for $\mathbf{x}^{\prime}=A \mathbf{x}$ and hence, find $e^{A t}$. $$A=\left[\begin{array}{ll}2 & 1 \\0 & 2\end{array}\right]$$.
Use the techniques from Section 9.4 and Section 9.5 to determine a fundamental matrix for $\mathbf{x}^{\prime}=A \mathbf{x}$ and hence, find $e^{A t}$. $$A=\left[\begin{array}{ll}2 & 1 \\0 & 2\end{array}\right]$$....
5 answers
What category have scientists assigned are organisms that canlive in extreme conditions?
What category have scientists assigned are organisms that can live in extreme conditions?...
5 answers
What is shielding? In an atom, which electrons tend to do the most shielding (core electrons or valence electrons)?
What is shielding? In an atom, which electrons tend to do the most shielding (core electrons or valence electrons)?...
5 answers
Distribute your circuit on board and connect ements with wires Vcc ~ISVRc IOKOLOOKO10pF10pF2N2222NIFETblock OUT~KQKAIKFigure 3Find Ine voltage gaincascade amplifiertermsshownFigure 2 Set oscilloscope display in XY mode draw the Vout Vin graph as shown in XY mode osc. display:Find the total current drawn from power supply for the circuit in Figure Be careful; current is drawn by both transistors -BJT, JFET
Distribute your circuit on board and connect ements with wires Vcc ~ISV Rc IOKO LOOKO 10pF 10pF 2N2222 NIFETblock OUT ~KQ KA IK Figure 3 Find Ine voltage gain cascade amplifier terms shown Figure 2 Set oscilloscope display in XY mode draw the Vout Vin graph as shown in XY mode osc. display: Find ...
5 answers
12 If tan & =<a< 909 , then find the exact value of each of the following:a. sin 2b. cOs 2C.tan 2a.sin 2 (Simplify your answer; including any radicals. Use integers or fractions for any numbers inb. cos 2 (Simplify your answer; including any radicals Use integers or fractions for any numbers in thtan 2 (Simplify your answer; including any radicals. Use integers or fractions for any numbers in theEnter your answer in each of the answer boxes
12 If tan & = <a< 909 , then find the exact value of each of the following: a. sin 2 b. cOs 2 C.tan 2 a.sin 2 (Simplify your answer; including any radicals. Use integers or fractions for any numbers in b. cos 2 (Simplify your answer; including any radicals Use integers or fractions for any...
5 answers
Nitration (HNO3- HzSO4) of Chlorobenzene will form how many products? CIOne para onlyOne ortho and one ParaOne meta productOne ortho only
Nitration (HNO3- HzSO4) of Chlorobenzene will form how many products? CI One para only One ortho and one Para One meta product One ortho only...
5 answers
Balance the following chemical reaction:NazCOz (aq)+CaClz (aq) CaCOz (s)+NaCl (aq)Determine the molar mass of calcium chloride; CaClz Show your wOrkDetermine the molar mass of calcium chloride; CaCO: Show your workDetermine the molar mass of sodium carbonate NazCOz Show youI work
Balance the following chemical reaction: NazCOz (aq)+CaClz (aq) CaCOz (s)+NaCl (aq) Determine the molar mass of calcium chloride; CaClz Show your wOrk Determine the molar mass of calcium chloride; CaCO: Show your work Determine the molar mass of sodium carbonate NazCOz Show youI work...

-- 0.020993--