3:- Find the maximum value of the function f(x, y) = x²y on the line x + y = 3.

Q: Suppose that f(x, y) = x² − xy + y² − 5x + 5y with x² + y² ≤ 25. 1. Absolute minimum of f(x, y) is…

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Q: Find the values of x, y, z at which f (x, y, z) = x2 + 4y2 + 5z2 - 6x + 8y + 3 assumes its minimum…

A: f(x, y, z)=x2+4y2+5z2-6x+8y+3   we have to find all points of x, y, z Taking, ∂f∂x=0, ∂f∂y=0 and…

Q: Find the point on the planez = x + y + 1closest to the point P = (1, 0, 0). Hint: Minimize the…

A: Let Q(x,y,z) be the point closest to the point P. Let D be the distance between these two points.…

Q: Find the absolute maximum and minimum of the function f(x,y) = 4y² + 18x – 18 over the closed region…

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Q: Find the point where the maximum value of f(x, y) = xy subject to y = 33 – x² occurs. (x, y, z) =

A: (x,y,z) = (√11,  22,  22√11)  The detailed solution is as follows below:

Q: The function f (x, y) = 2x + 3y + 9 - x2 - xy - y2 has a maximum at some point (x, y). Find the…

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Q: Find all points (x, y) where f(x, y) has a possible relative maximum or minimum.

A: We have to find the critical points for the function f(x,y)=-x2+2y2+6x-8y+5.

Q: Find the maximum and minimum values of the function f(x, y) g(x, y) = x² + xy + y² = 27 ry subject…

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Q: 8, find the the function maximum value of +(x, y,Z) 2179`x+ 2y -12+7 subJect to Constrain t+3 +2² =…

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Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: Suppose that f(x, y) = x² + y° at which 0 < x, y and 1x + 8y < 7. 1. Absolute minimum of f(x, y) is…

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Q: Find the local minimum value of f(x, y) = 4 + a" + yl – 11ry.

A: Use double derivatives test to find local maximum or minima.

Q: Find the absolute maximum and minimum of the function f (x , y) =x² + y² on a closed triangular…

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Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 2x + 9y < 8. 1. Absolute minimum of f(x, y) is…

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Q: Find the absolute maximum and minimum of f(x, y) = 3z +y within the domain z² +y? < 4.

A: Use lagrange multiplier.

Q: Examine for minimum and maximum values of f(x,y,z)=2xyz-4xz-2yz+x^2+y^2+z^2-2x-4y+4z

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Q: Find the slope of the curve y=x2−3x−4 at the point ​P(2​,−6​) by finding the limiting value of the…

A: Giveny= x2-3x-4 = f(x)at point ( 2, -6)as f(x) =x2-3x-yand f(2+h) = (2+h)2-3(x+h) -4…

Q: Suppose that f(x, y) = x² + y? at which 0 < x, y and 5x + 6y < 8. 1. Absolute minimum of f(x, y) is…

A: This question is related to linear programming, we will solve it using given information.

Q: Find the absolute maximum of f(x,y) = 7x²y² + 5y² + 9x² bounded by y = x, y = 0 and x = 2.

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Q: Find the absolute maximum and minimum of the function on the given domain. f(x.y) = 6x + 5y on the…

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Q: Find the local minimum value of f(x, y) = 4+ xl+yl1 11æy. -

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Q: Find the local minimum value of f(x, y) = 4+ x³ + y³ – 5xy.

A: Explanation of the answer is as follows

Q: Find A and B so that f(x, y) = x2 + Ax + y² + B has a local minimum at the point (4, 0), with…

A: Given function of two variables is f(x,y)=x2+Ax+y2+B it has local minimum point at (4,0) and minima…

Q: Find the maximum value of  f(x,y)=3xy(5−10x−5y) over the triangle with vertices (0,0), (1/2,0) and…

A: Given :            f(x, y)= 3xy(5-10x-5y)            Vertices (0, 0) (1/2, 0) and (0, 1)

Q: Find the relative maximum or minimum value (if any) of f(x, y) = (x2 + y)ey/2

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Q: Suppose that f(x, y, z) = 2x + 5y + 4z at which a2 + y? + z2 < 12. 1. Absolute minimum of f(x, y, z)…

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Q: Identify the critical points of the function f(x, y) = x³ – 12x +y² – 3xy + 30 and the local minimum…

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Q: Maximize F=x+y subject to:  x+2y≤8  x≤6  x, y ≥0 Corner points at ____________________ Maximum…

A: We have to find maximum.

Q: Consider the function f(x, y) = y6 - 3x²y + 3x² Compute the stationary points of the function f(x,…

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Q: Find the absolute maximum and minimum of the function f(x,y) = 2x² - 4x + y² - 4y +6 on the closed…

A: Given that a function f( x , y ) =2x2-4x+y2-4y+6  on the closed triangular plate bounded by the…

Q: Find the critical point of the function f(x, y) = V 8x2 + 5y2 . Determine whether it is a minimum,…

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Q: Find the point where the function f(x,y, z) = x + 2y + 3z subject to the I takes on its minimum…

A: The given function is f(x,y,z)=x+2y+3z.

Q: Find all points (x,y) where f(x.y) has a possible relative maximum or minimum. f(x.y) = x* - 32xy +…

A: Solution:Given thatfx,y=x4 -32xy+8y2-10we have to find all points x,y where fx,y has a possible…

Q: Find the minimum value ofx +y +z² given x+y+z=3a.

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

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Q: Find the absolute maximum of f(x,y) = 3x2y2 + 2y2 + 2x2 bounded by y = x, y = 0 and x = 5.

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Q: Find the maximum and minimum attained by f(x, y) = 3xy + 2x + 3y in x2 + y < 1. You must use…

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Q: Determine the critical point and its type of function f with f (x, y) = 3x^2y + y^3 − 3x^2 − 3y^2 +…

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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: Suppose that f(x, y) = x² – ry + y² – 5x + 5y with x² + y? < 52. 1. Absolute minimum of f(x, y) is…

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Q: Find the absolute maximum and minimum of the function f(x,y) = 2x - 8x + y - 8y + 2 on the closed…

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Q: Find the point where the minimum value of f(x, y) = xy subject to y = 90 – x occurs.

A: Find the point where the function f(x,y)=xy subject to y=90-x2 attains its minimum value.

Q: The function f(x, y) = -2x² + 4y² - 11 has a local minimum at the point (0, 0). Select one: True…

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Q: Find the maximum slope on the graph of f(x, y) = 2 sin(ry) at the point P(4, 0).

A: The given question can be solved as shown in step2.

Q: Suppose that f(x, y, z) = 3x + 3y + 4z at which a² + y² + . < 52. 1. Absolute minimum of f(x, y, z)…

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Q: = 1 Find the minimum value of f(x, y, z) = 3x − y − 3z subject to x² + 2z² - - and x + y -z = 0.

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Q: Does the function f(r,y) = e-(z²+y°) achieve an absolute minimum on D= R²? %3D

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Q: Find the point where the maximum value of f(x, y) = xy subject to x + 5y = 74 occurs. (x, y, z) = |

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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.

Q: Find the maximum value of J (x) f(x) = V1 + x² on the indicated interval. [0,2]

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