Maximize and minimize the function f (x, y) = 1+ 4x + 2y – 2x2 – y? on the triangle bounded by the lines x = 0, y = 0, and y = 6 – x, along with its interior. %3D

Q: 5. Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

A: Answer

Q: Find the maximum and minimum values of the function on the rectanglar region: −1≤x≤1,−2≤y≤2.…

A: Given function is f(x,y)=4x2-y2differentiate partially w.r.t.x,fx(x,y)=8xfy(x,y)=-2yfind the…

Q: D={(1,y) | + 등아 < 6}. 25

A: Use lagarange multipliers

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: The maximum value of the function f (x, y) = x2 + 2y2 - x in the region x2 + y2 < 1 %3D

A: Answer

Q: Find the absolute maximum and absolute minimum values of the function f(x, y) = x4 + y4 − 4xy on the…

A: Consider the equation

Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) = x2 + y? subject to the…

A: Given f(x,y)=x2+y2 and subject to constraint is xy=2 and we need to find the minimum value of given…

Q: Q1/ Use Lagrange multipliers to find any maximum or minimum volumes: i) z = f(x,y) = 5 – 3x – 4y and…

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Q: Use Lagrange multipliers to find the minimum and maximum values of the function f(x,y,z)=xyz on the…

A: Given, f(x,y,z)=xyz    and g(x,y,z)= x2+y2+z2=9 we have to find the minimum and maximum values of…

Q: Find the absolute maximum and minimum values of the function f (x, y) = x – y + xy on the closed…

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Q: Use the Lagrangian method to minimize f(x, y, z) = x² + 2y² + z² s.t. x² + 2y + 3z = 8 Find the…

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Q: Maximize and minimize f(x, y, z) 3x + y + 2z subject to 2x + 3y2 + 4z² 210 %3D

A: We have to use lagrange multipliers.

Q: 2) f(x, y) = x +y on the closed triangular plate bounded by the lines x 0, y= 0, y+2x = 2 in the…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Find the absolute maximum and minimum values of f(x, y)=x² +xy+y² -6y on D={(x, y)| -3<x<3, 0<y<5}.

A: Given curve is f(x,y) = x^2+y^2+xy-6y  Find critical points

Q: Find the maximum and minimum values of the function f(x, y) = xy onthe disk V = {(x, y) : x 2 + y2…

A: The given function is, fx,y=xyon the disk V=x,y:x2+y2&lt;1 fx=λgxfy=λgygx,y=1…

Q: Maximize the function f(x, y, z) = x² – y², given that x² + 2y² + 3z² = 1. %3D

A: Here, we can use Lagrange multiplier to maximize f(x,y,z)=x2-y2 with constraint x2+2y2+3z2=1. Let…

Q: Find the absolute extrema of the function f(x, y) = x² + y? – 2x on the triangular region with…

A: The shaded part represents the region with the given vertices. We observe that our critical point…

Q: Find positive numbers x and y such that x + y = 48 and 5x2y + 10 is maximized.

A: Given that, x + y= 48 y = 48 - x ................... (1) The function is: f(x, y) = 5x2 y+ 10 f(x) =…

Q: linearize the nonlinear equation in the region defined by 4 < x < 5, 3 < y < 4 z = y?Vx + 5e(3x-y²)

A: Given, z=y2x+5e3x-y2 The goal is to linearize the given equation around the operating point,…

Q: (c) Find the minimum and maximum value of f(x, y, z) = xy + yz.

A: Given: The function fx,y,z=xy+yz   To find: The minimum and maximum value of the given function

Q: Maximize f (x, y) = x + y subject to g (x, y) = x² + y = 4

A: Given function fx,y=x+y......(1) gx,y=x2+y2=4......(2) Applying the Lagrange multiplier, note that…

Q: Find the maximum and minimum values of f(x, y) = 2x + y - 3xy onthe unit square V = {(x, y) : 0 &lt;…

A: To find the maximum and minimum value of f(x,y)

Q: Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Minimize:…

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Q: 1. Find minimum value of f (r, y) = 2x+3y-6ry on the unit square D = {(x, y) : 0 < r, y < 1}.

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Minimize z = 4x + y y+ 5x 10 8y + 4x > 40 Subject to y + x Minimum is at AL ALALALAI %3D

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Q: Picture attached. Thanks in advance!

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Q: The maximum value of the function f (x,y) = x² + 2y² – x in the region x2 + y² < 1 O 3/2 O 9/4 O…

A: The maximum value is 9/4

Q: q Find a positive numbers x and y such that x²+y= 48 and their product P(xjy) = xy is maximized. %3D

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Q: Find the absolute extrema of the function f(x, y) = x2 + y? 2x on the triangular region with…

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Q: Use the method of Lagrange multipliers to maximize the function Maximize the function f(x, y) = xy²…

A: Here we have to use the Lagrange multiplier to maximize the function f(x,y)=xy2 and subject to…

Q: Find the absolute maximum and minimum values of D(x,y)=x²-xy + y² + 1 On the closed triangular plate…

A: Here I am using basic calculus we and also use short method.

Q: Maximize f(x, y, z) = x² + y² +z? Constrain x+2z = 6, x+ y =12

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A: Given that , fx,y,z=x2+y2+z2 and constraint is x+y+z-27=0 find the extrema using Lagrange…

Q: Find the absolute extrema of the function f(x, y) = x² + y? – 2x on the triangular region with…

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Q: Use Lagrange multipliers to find the maximum or minimum values of th f(x, y, z) = 2x + 2y + 6z; x2 +…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

A: here is the solution:

Q: Find the absolute extrema of the function f(x,y) = xy - x - 3y on the triangular region with…

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Q: Find x = that minimizes q(x) = x² – xy + y² subject to %3D the condition ||x|| = 1 , %3D

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = x2 + y? subject to ry =…

A: Given function is fx,y=x2+y2 and constraint is xy=1

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A: This is a problem of maxima and minima. Based on the general formula we will find out the value.

Q: Q5) Find the absolute maximum and minimum values of D(x,y) = x² - xy + y² + 1 On the closed…

A: Given: D(x,y)=x2-xy+y2+1

Q: Use Lagrange multipliers to maximize the function f(x, y) subject to t x. v) = xy - 2x2 - y, x+y =…

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Q: minimize subject to (xyz)-¹ x + 2y + 2z ≤ 72 x, y, z 20

A: Since you have posted multiple questions, we will solve only the first question for you.

Q: Minimize f(x,y,z) = x + 2y + 4z subject to the condition ** +y“ +z* = 7

A: Hello, thanks for your question .According to our policy I m doing the very first question . Please…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

A: Given;  Minimize :(x, y) =x2+y2 Constraint: x+2y-20=0.

Q: Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Minimize…

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Q: on Find the absolute minimum and maximum of the function f(x, y) = 2x¹ - xy² + 2y² the region 0≤x≤…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positiv Maximize…

A: The given function is;  f(x,y)=sqrt(43-x2-y2) Constraint: x+y-6=0