Find the two positive x and y such that x+y=60 and xy2 is maximum

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

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Q: Find the maximum value of s = xy + yz + xz where x + y + z = 6.

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Q: D={(1,y) | + 등아 < 6}. 25

A: Use lagarange multipliers

Q: Find two positive numbers x and y such that x+y=60 and xy^3 is maximum.

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Q: Find all points (x.y) where f(x.y) may have a maximum or minimum. f(x,y) = - 3x + 5xy- 2y² +x+y

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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: 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 positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

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 absolute maximum of f(x,y) = 6x²y² + 4y2 + 4x2 bounded by y = x, y = 0 and x = 2. %3D

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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: Suppose that f(x, y) = x² + y² at which 0 < x, y and 4x + 8y < 8. 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) = 7y + 64x – 3 over the closed region…

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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 f(x, y) = 4x2 + 2xy 3y2 on the unit square 0 sx s1, 0 sy…

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Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

A: f(x) = ax3 + bx2 + cx + d f(x) = 3ax2 + 2bx + c Now, f(x) = 0  at x = -2, 1 Hence , roots of above…

Q: Find 3 numbers x, y, and z such that their sum is 32 and P=xy^2z is a maximum.

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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: 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: Use the Lagrange method to find three positive numbers x, y, z such that x+y +z = 90 and x 2 yz is a…

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Q: Find the minimum and maximum values of: f (x, y) = x² + xy bounded by the graphs y = x´ and y =9

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Q: Find the local minimum value of f(z, y) = 4 + x² + y7 – 7xy.

A: Explanation of the answer is as follows

Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 4x + 7y < 9. 1. Absolute minimum of f(x, y) is…

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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: 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: Find the maximum value of f(x, y, z) = y - z Subject to x + y + z = 1,x² + y² = 1 O - √5 + 1 O-√5-1…

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Q: The sum, of three numbers is constant. Prove that their product is a maximum when they are e v and z…

A: That is to maximize f(x,y,z)=xyz Now, x+y+z=K Let g(x,y,z)=x+y+z-K=0

Q: + A(- for 0<x< 1, then u attains its maximum in the interval 0 sxs1 either at x=0 or at x= 1.

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Q: Find the absolute maximum and minimum values of the function on the triangular region whose vertices…

A: The given function f(x, y) is a polynomial and therefore, it is continuous and has both maximum and…

Q: Find the absolute maximum and minimum values off on D, where f(x, y) = x – 2xy+2y and D={(x,…

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

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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 extreme values of the function f (x, y) = e¬¤y given that (x, y) must live in the region…

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Q: Find all points (x,y) where f(x,y) has a possible relative maximum or minimum. f(x,y) = x4 - 4xy +…

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Q: find the number/s in the interval I=[1/2,3] sych that the sum of the number and its reciprocal is a…

A: Let us consider x be the number And its reciprocal is 1x​ Now the sum of the number and its…

Q: The function f(x, y) = -2x² + 4y² - 12 has a local maximum at the point (0,0). Select one: O True…

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

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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 absolute maximum of f(x,y) = 9x²y² + 4y2 + 4x² bounded by y = x, y = 0 anC Answer:

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Q: Find the absolute maximum of f(x,y) = 5x²y² + 4y² + 6x² bounded by y = x, y = 0 and x = 4. %3D…

A: The given function is: f(x,y)=5x2y2+4y2+6x2Bounded Region is:  y=x,  y=0,  x=4

Q: Determine the values of constanas a,b,c, and d so that f(x) = ax^3 +bx^2+cx+d has a local maximum at…

A: Given that f(x) = ax3 +bx2 + cx + d has a local maximum at the point (0,0) and a local minimum at…

Q: Find the relative maximum and minimum values. f(x,y) = x° +y° - 3xy

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Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 5x + 6y < 7. 1. Absolute minimum of f(x, y) is…

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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: Let f(x, y) = g(x) + h(y) where g(x) and h(y) are positive. If g(x₁) ≥ g(x)and h(yo) ≥ h(y) then…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.