Find the minimum and maximum of y = f(x) = x³ – x² – 3x + 2

Q: Find the minimum value of the function f (x, y) = 16x² + 81y? subject to the constraint xy = 1.

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Q: Find the local minimum and maximum of y= x2/ 3 + x2

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Q: Find the maximum value of z = xy2 subject to 2x2 + y2 = 294; x ≥ 0, y ≥ 0. z =

A: Given information : z = xy2  subject to  2x2 + y2 = 294;  x≥0;  y≥0.

Q: Find the maximum and minimum value of f(x,y) =x3+3xy2-3x2-3y2+4

A: fx,y=x3+3xy2-3x2-3y2+4   fx=3x2+3y2-6x   fxx=6x-6   fxy=6y   fy=6xy-6y   fyy=6x-6

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: Find the maximum value of xy if it is required that 2x +7y = 35

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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: 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: 5. y2 2x y26-x fx, y) = 4x+ 3y Minimum: Maximum: | | | | |

A: We need to find maximum and minimum values of f(x,y).

Q: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

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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 minimum value of x²+y² + z²,

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Q: Find the minimum value of f(x,y)=66x2+9y2 subject to the constraint x2+y2-784

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Q: Find the relative maximum and minimum values. f(x.y)= 8xy-x - 4y

A: Given :f(x,y)=8xy-x3-4y2

Q: If f'(x) = x - 2x² - x +2, thenf has a relative minimum at x= 1 -1 2 -2

A: The answer is

Q: Find the maximum of f (x, y, z) = z subject to the two constraints x2 + y2 = 1 and x + y + z = l.

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Q: Let f (x)=x* + 2.x³ – 3.x² – 4.x + 4. Find: (b).. the points at which f (x) has a relative maximum…

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

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Q: Find the extreme values of the function f(x,y,z) = x4 + y4 + z4, subject to the constraint x2 + y2 +…

A: Given,  f(x,y,z) = x4+ y4 + z4,  Subject to the constraints  g(x,y,z)= x2 + y2 + z2 =1. Now we find…

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

A: Recall:  Method of Lagrange Multipliers: To find the extremum values of f(x, y) subject to…

Q: Use Lagrange multipliers to find the minimum value of f(x,y) x2 – y? subject to the constraint 2y –…

A: According to question, fx, y = x2 -y2,subject to the constraint 2y-x2 = 0,let gx, y = 2y-x2

Q: Find the relative maximum and minimum values. Зx2 f(x,y) = + 10y2 + 3

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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: 1. Find the maximum value of f(x, y) = 4xy where x > 0 and y > 0, subject to the constraint 9. = 1.

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Q: What are the local max and minimum points of y=x^3-3x+1

A: The given function is: y=x3-3x+1

Q: Find a constrained minimum or maximum of the function f(x, y) = xy subject to the constraint 4x? +y²…

A: Consider gx,y=4x2+y2 and evaluate the partial derivatives of fx,y and gx,y with respect to x and y.…

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: The function f(x, y) = 2x2+y2 has an absolute maximum and absolute minimum subject to the constraint…

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Q: Find the minimum of the function f(x, y) = x² + y² – xy subject to the constraint 2æ + 2y = 2. Value…

A: We have to find the minimum of the function fx,y=x2+y2-xy subject to the constraint 2x+2y=2.

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

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Q: The function f(x,y)=e^6xy has an absolute maximum value and absolute minimum value subject to the…

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Q: Given f (x)= (x^2) (e^-x) , find the relative maximum and relative minimum point respectively.

A: We will use derivative to find maximum and minimum value for the function. If f(x) is a function.…

Q: Find the relative minimum f(x,y)=288y2+x2-x2y

A: According to the given information it is requires to find the relative minimum of the function:

Q: Find the values of constants a, b, and c so that the graph of y = (x2 + a)/(bx + c) has a local…

A: given

Q: Determine the extremum points and the values of the maximum and minimum of the function + f(x, y) :…

A: Given:  f(x,y)=xy+yx;   g(x,y)=x2+y2-8=0So,…

Q: Find the absolute minimum value of the function f(x, y) x+ 4y2 = 9. 2x + 3y subject to the…

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Q: Consider the function f(x, y) = &x² – 8y² subject to the conditionx? + y² = 9. Use Lagrange…

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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: Use Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = xy subject…

A: Given  objective function f(x,y)= xy  constraint  g(x,y)= 9x2+y2-4

Q: The function f(x,y) = 7xy has an absolute maximum value and absolute minimum value subject to the…

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Q: Find the absolute maximum and the absolute minimum of the function f(x,y, z) x² + y² + z², subject…

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Q: Find the relative maximum and minimum values. f(x,y) = x² +y2 +4x- 12y

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Q: Find the closest and most distant points to the origin on the curve x^2+xy+y^2=1.   Use lagrange…

A: Given that the curve is x2+xy+y2=1. It is required to find the closest and most distant points to…

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

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Q: Minimize f(x,y)=x2-y2 subject to the contraint 3x-7y=-4 when the minimum occurs, what is  a. x?…

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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: If f'(x) = x³ – 2x² – x + 2, then f has a relative minimum at x

A: f'(x)=x3-2x2-x+2, we have to find relative minimum of f.

Q: Find the maxima and/or minima of f (x, y,z) = 2x2 + y2 + 3z2 subject to the constraint 2x - 3y - 4z…

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