1. Find the absolute minimum value of 0 < x < 4 f (x, y) = 4x² + 2xy – 2y? – 18x on the rectangular regic where and 0< y< 3. Lustify vour answer

Q: Find the maximum and minimum values of the function f(x, y) = 3y² + 2x² – 6y %3D in the region where…

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Q: Find the absolute minimum and maximum values of f(x,y) = 4x^2 + y^2 on the disk x^2 + y^2 &lt;= 1.

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Q: 6. Find the absolute maximum and minimum of the function f (x, y, 2) = x + 2y on the intersection…

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Q: Suppose f(x, y, z) = In(7x + 9y+7z). Find an equation for the level surface of f that passes through…

A: Given Data: The level of the curve for fx,y,z=In 7x2+9y+7z2 is of the form,…

Q: (b) By minimizing the function f(x, y, u, v) = (1 – u)² + (y – v)² subject to the constraints y =…

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Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: Find the absolute minimum and absolute maximum of the function f(x, y) = x^3 – 2y^3 + 3y + (x – 1)^2…

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Q: Find the local minimum value of f(x,y) 4x2 + 3y2+ 2x + 2y + 4. Give your answer correct to two…

A: The given function is f(x,y)=4x2+3y2+2x+2y+4

Q: Let f(x, y) = x* + 2x² – a – ay + y² – 5y and let D be the closed rectangle with 0 < # < 5 and 3 <…

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Q: Find absolute maximum and minimum values for f (x, y) = x² + 14xy + y, defined on the disc D = {(x,…

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Q: Find constants a and b so that the minimum for the parabola f(x) = x- + ax + bis at the point (5,…

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Q: 1- Find the minimum and maximum values of the function f(x,y) = 2x2 + 3xy + 2y2 + x - y inside and…

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Q: 3. Describe the level surfaces of the function. f(x, y, 2) = x² + 4y? + 42?

A: We Know that,  A level surface of a function w = f(x, y, z) with three variables is a surface f(x,…

Q: 6. Find the positively oriented simple closed curve C for which th value of the line integral I 4 –…

A: Consider the given integral. I=∫Cy3−ydx−2x3dy Apply the green theorem. ∫CPdx−Qdy=∬D∂Q∂x−∂P∂ydA…

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: The subject to constraint can be used to find the value of y and then plugging it into the function…

Q: Find and identify all critical points for the function f(x, y) = 4:r³ + 2ry? + 1022 + 2y? as a local…

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Q: Suppose that f(z, y) = z² - zy + y? – 5z + 5y with z? + y? < 25. 25 1. Absolute minimum of f(x, y)…

A: We have to solve the maxima minima problem.

Q: 6. Find a cubic function f(r) = ar³ + bx² + cx +d that has a local maximum value of 3 at r =-2 and a…

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Q: 1 in the first quadrant x>0, y>0. ху Find the minimum value of f (x, y) =x+8y+- -How do you know…

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Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. f(x.y) =x - 5xy + 6y…

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Q: 16. Let h(x, y) = xy – 2x². Find the minimum and maximum values of h on the rectangle where 0 < x <…

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Q: Find the maximum and minimum values of f(x, y) = x² + 2y² on the quarter circle x² + y² ≤ 4 with r,…

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Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x+4) in the interval…

A: Given: y=2x-123x+4

Q: 18. Find the absolute maximum and absolute minimum values for the function f (x,y) = e-**-y* (x² +…

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Q: Find the local minimum value of f(x,y) = 3x² + 2y2+ Ox + 2y + -5. Give your answer correct to two…

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Q: Find the extreme values of g(x,y,z) = 2x² + xy + 4y² + xz + z² + 2. %3D and determine whether the…

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Q: fhas a local minimum at x = (A) 0 (В) 1 (C) 2 (D) 3 (E) 5 fhas a point of inflection at x = (A) 1…

A: Given:Graph

Q: Find the absolute maximum and minimum of f(x,y)= 4xy^2 - (x^2)(y^2) - xy^3 on the closed triangular…

A: f(x,y)=4xy2-x2y2-xy3fx=4y2-2xy2-y3fx=04y2-2xy2-y3=04-2x-y=0…

Q: 10 نقاط Check whether the following points: {(0,0), G5.E=)} indicate a maximum, minimum or saddle…

A: Solution:-

Q: Find the maximum and minimum values attained by f(x, y, z) = 2xyz on the unit ball x2 + y2 + z2 < 1.…

A: fx,y,z=2xyz on the unit ball x2+y2+z2≤1 gx,y,z=x2+y2+z2-1 ∇f=∂f∂x,∂f∂y,∂f∂z ∇g=2yz,2xz,2yx…

Q: (ii) Find the extremum of Z= x2 +y2 subject to x + 4y 2 and examine whether the %3D %3D stationary…

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Q: Determine the maximum and minimum values of f(x,y,z) = 3x + 6y + 2z, subject to 2x^2 + 4y^2 + z^2 =…

A: Using the lagrange multipliers

Q: 4 3.2x Y=x'e write the point where it is the absolute minimum with and Coordinetes. the

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Q: 2 Find the point onthe curve y=Jx that is. the point (4,0). minimum distance from a

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Q: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

Q: (x) has absolute minimum on (0,5) at x = A) 5 B) 4 C) 0 D) - 4

A: From the given problem:   fx=x2-8x+1 ; 0,5   First, differentiate the given function and equate it…

Q: st, enter DNE.) f(x, y) = x² + y² + 4x 10y6 minimum maximum point (x, y, z) = (x, y, z) = (x, y, z)…

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Q: Find a, b, c, and d such that the cubic function f(x) = ax³ + bx² + cx + d satisfies the given…

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Q: A rectangular plate with an area of 36 cm? is to be produced on a lathe in such a way that the…

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Q: 2) a) Find the absolute maximum and minimum values of the function f(x, y) = e*+y* in the disk x? +…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: Let f(x,y)= 3+cos(x) sin(2y) a) Show that the function has a stationary point at (0,Pi/4). b) Is (0,…

A: To analyze the critical point (0,pi/4) of the given function of two variables

Q: Suppose that f(x, y) = x² + y at which 0 < x, y and 3x + 9y < 7. 1. Absolute minimum of f(x, y) is…

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Q: 5) Let R(x, y) = 3x² + y². Find the minimum value of R on the hyperbola xy 2.

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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: Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular…

A: Given:- The function is, f(x,y)=3xy-3x-6y+1on the closed triangular region whose vertices are (0,0),…

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: We have to find maximum and minimum values using Lagrange multipliers

Q: 20. Find the minimum value of ry+xz+ yz given that r, y, z are real numbers that satisfies the…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: 1o9.. 10 11 12 What is the minimum value of y = -3 – 5 sin (4x)?

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Q: Find the absolute maximum value and absolute minimum value of f(x, y) = x² + 2xy – 4x + 2y? – 8y +…

A: We have to find the absolute maximum and absolute minimum value of the given function.

Q: If x² + y² < z < 1, find the maximum and minimum of the function u(x, y, z) = x + y + z

A: We have to find the maximum and minimum of the function.