Answer to The critical points for f(x, y) = xy x^2 y^2 2x 2y 4 are A, (1, 1) min, (2, 1) max B, (2, 2) min C, (2, 2 Skip Navigation Chegg homeNov , 11 · F(x,y) = 3xy x^2y xy^2 Maximum and minimum values and saddle points of the function So I understand that I have to find partial derivatives to respect to x and y to find the critical points ok, after I found the partial derivatives, I set them equal to 0 then I was stuck I don't know how to do substitution with the partial derivatives f_x(x,y) = 3y 2xy y^2 f_y(x,y) = 3x xThis is the graph of y = f(x) First I want to label the coordinates of some points on the graph Since, for each point on the graph, the x and y coordinates are related by y = f(x), I can put the coordinates of these points in a list x y = f(x)4 1 1 1 2 0 31

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F(x y)=xy-x^2-y^2-2x-2y 4
F(x y)=xy-x^2-y^2-2x-2y 4-F (xy)f (x) = f (y) 2xy If we divide both sides by y, and take the limit of both sides, as y approaches 0, we get f' (x)= 2x (limit as y→0) f (y)/y Since f (0) is 0 from the initial conditions (put x=y=0 in the original expression), we have a 0/0Free equations calculator solve linear, quadratic, polynomial, radical, exponential and logarithmic equations with all the steps Type in any equation to get the solution, steps and graph



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If f(x;y) can be made arbitrarily close to L by taking (x;y) su ciently close to (a;b) Note Recall that lim x !a f(x) exists if and only if lim x a f(x) = lim f(x) We can only approach x = a from two directions However, for functions of two variables, there are in nitely manyProblem 12 Easy Difficulty If $ f(x, y) = \sqrt{4 x^2 4y^2} $, find $ f_x(1, 0) $ and $ f_y(1, 0) $ and interpret these numbers as slopes Illustrate with either handdrawn sketches or(b) x 6 – y 6 = (x 3) 2 – (y 3) 2 = (x 3 y 3)(x 3 – y 3), by (1) = (x y)(x 2 – xy y 2)(x y)(x 2 xy y 2), by (2) and (3) Which of the above factorization is correct?
Jul 17, 17 · x = y If y is a root, then (x y) is a factor Since it is the only one, then the quadratic is a perfect square (as indicated by the 0 under the square root) x^2 2xy y^2 = (x y)(x y) = (x y)^2"y is a root" simply means that the only way we can get the thing to add up to zero, is to make x = y for example, if x = 3 and y = 3This is always true with real numbers, but not always for imaginary numbers We have ( x y) 2 = ( x y) ( x y) = x y x y = x x y y = x 2 × y 2 (xy)^2= (xy) (xy)=x {\color {#D61F06} {yx}} y=x {\color {#D61F06} {xy}}y=x^2 \times y^2\ _\square (xy)2 = (xy)(xy) = xyxy = xxyy = x2 ×y2 For noncommutative operators under some algebraicJNTU BTech M2 Maths and Bsc Maths Chapter Partial Differentiation Topic Maximum and MinimumExamine the function f(x ,y)=x^4y^42x ^24xy2y^2 for ext
Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history(0 , 0) , (1 , 1) and (1 , 1) We now determine the second order partial derivatives f xx (x,y) = 4 f yy (x,y) = 12y 2 f xy (x,y) = 4 We now use a table to study the signs of D and f xx (a,b) and use the above theorem to decide on whether a given critical point isHow to solve Find all local extreme values for A) f(x, y) = xy x^2 y^2 2x 2y 4 B) g(x, y) = 3y^2 2y^3 3x^2 6xy By signing up,



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Feb 17, 17 · Explanation The theory to identify the extrema of z = f (x,y) is Solve simultaneously the critical equations ∂f ∂x = ∂f ∂y = 0 (ie zx = zy = 0) Evaluate f xx,f yy and f xy( = f yx) at each of these critical points Hence evaluate Δ = f xxf yy − f 2 xy at each of these points Determine the nature of the extrema;Question Can you help me solve the equation (2x^2xyy^2=8)and(xy=4) I have to find the value of x and y I'm having trouble solving this particular problem I just know the answer has to have 4 solutionsFind the extreme value of the function f(x,y) = xy x^2 y^2 2x 2y 4 Get the answers you need, now!



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1st x2y=0 2nd y=2x3Rewrite 2nd as follows 3rd 2xy=3 Multiply 1st by 2 to get 4th 2x4y=0 Subtract 4th from 3rd to get 5th 3y=3 y=1 Substitute this value into 1st to solve for x x2(1)=0 x=2 Solution (2,1) Cheers, Stan HCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history43 x 2 2xy y 2 is a perfect square It factors into (xy)•(xy) which is another way of writing (xy) 2 How to recognize a perfect square trinomial • It has three terms • Two of its terms are perfect squares themselves • The remaining term is twice the product of the square roots of the other two terms Final result x • (2x y



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1) is a critical point The second derivative test f xx = 2;f yy = 2;f xy = 0 shows this a local minimum withF(x,y)=xy over the region D = {(x,y) x2 y2 8} As before, we will find the critical points of f over DThen,we'llrestrictf to the boundary of D and find all extreme values It is in this second step that we will use Lagrange multipliers The region D is a circle of radius 2 p 2 • fx(x,y)=y • fy(x,y)=xProof f(x, y) = xy(x 2 − y 2) / (x 2 y 2) continuous everywhere Let f(x, y) = xy(x2 − y2) / (x2 y2) with f(0, 0) = 0 The question was asking to proof f(x, y) continuous everywhere One way to solve it was to just change x = rcos(θ), y = rsin(θ) and solved it


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We know that $(x2y)(x2y)=4$ and that $(x2y)(x2y)=x^24y^2$ Thus, Quantity A MUST be equal to $4$, which is less than Quantity B The correct answer is B, Quantity B is greater What Did We Learn Coincidental mathematical relationshipsDec 09, 11 · (a) Find y' by implicit differentiation (b) Solve the equation explicitly for y and differentiate to get y' in terms of x (c) Check that your solutions to part (a) and (b) are consistent by substituting the expression for y into your solution for part (a)Step by Step Solution Step 1 Equation at the end of step 1 (((((x2)xy)4x)2y2)y)3 Step 2 Trying to factor by pulling out 21 Factoring x2xy4x2y2y3 Thoughtfully split the expression at hand into groups, each group having two terms Group 1 2y24x



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