Find the maximum and minimum values of f(x, y)=x+3xy2-3x2-3y²+4.

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: What is the relative minimum value of the function f(x, y) = x³ – 3xy + y³ – 2?

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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 all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

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Q: Find the quadratic function f(x) = ax + bx +c that goes through (2,0) and has a local minimum at (0,…

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Q: Show that the function z = f (x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point.…

A: Given

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: 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 location (x, y) of the minimum of the function: f (x,y)=3x² – 3xr+5+1.5xy +5y² – 4y…

A: Given : function          fx, y=3x2-3x+5+1.5xy+5y2-4y To find : location x, y of the minimum of the…

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

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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 orthogonal trajectories of the curve x^(2) + y^(2) = c^(2)

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Q: Find the orthogonal trajectories of the functiony x + ce which is passing through (-2,0)

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Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

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Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

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Q: Suppose that f(z, y) = e-2-2y –2z+y Then the maximum is

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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 the quadratic function f (x) = ax2 + bx + c that goes through (0, 1) and has a local minimum at…

A: Given: The quadratic function fx=ax2+bx+cpasses through the point 0,1 and has local minimum at 1,-1,…

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 maximum rate of change of the function f(x,y) =4x^2-2y^3 at the point (1,1)

A: Given data: The given function is f(x,y)=4x2-2y3. The given point is (a, b)=(1, 1). The expression…

Q: Calculate the maximum and minimum of the function f (x,y) = xy subject to the condition x2 + y2 = 1

A: To find the optimal solution, we will use Lagrange multiplier method. The Lagrangian function is…

Q: Find the orthogonal trajectories for the family of curves. (Enter your solution in the form F(x, y)…

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Q: Find the maximum and minimum values of f(x, y) = (x- y) e- + y)

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Q: Find the minimum values of the function (x, y) = x² + 2y² that lic on the cirele x² + y² =1

A: Given : Function fx,y = x2 + 2y2  Circle x2 + y2 = 1   To find : Minimum values of the given…

Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

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

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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 orthogonal trajectories of x^2+y^2−2cy=0

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Q: Show that the function z = f(x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point.…

A: Given a function in two variablesz=fx,y=x3-3x2-4y2+2

Q: At what value of x does the curve y = x(x – a²)(x – b²) have a local maximum?

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Q: x² – y² = = CX

A: For orthogonal trajectories, replace dy/dx by -dx/dy and solve it.

Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: 2 f(x, y) = x² + 3xy

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Q: Find the maximum and minimum values of f(x,y) =xy constrained on x2+2y2=1

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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: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

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

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Q: 2) Find the relative maximum or minimum value of f(x, y) = 3x² + 2xy + 10y² - 54x - 308y

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

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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.