Find the maximum and the minimum for the given function f(x, y) = 4x2 - xy + 4y2 over the disk x2 + y2 < 2

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

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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: Find the maximum and minimum values of the function on the rectanglar region: −1≤x≤1,−2≤y≤2.…

A: Given function is f(x,y)=4x2-y2differentiate partially w.r.t.x,fx(x,y)=8xfy(x,y)=-2yfind the…

Q: Use Lagrange multipliers to find the maximum value of f(x, y, z)= xyz where x >0, y>0 and z>0,…

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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: 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 the maximum value and the minimum value of the function f(x, y, z) = x + y + z such that x2 +…

A: Given To find the maximum value and the minimum value of the function f(x, y, z) = x + y + z such…

Q: Find the absolute maximum and absolute minimum values of the function f(x, y) = x4 + y4 − 4xy on the…

A: Consider the equation

Q: Given the function f(x,y) =4 x – y on the convex region defined by R= {(x,y) : 3x + 3y 0, y > 0}…

A: To find: The maximum value of the function and find the coordinates where the function is maximum.…

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

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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 the absolute maximum and minimum values of the function f (x, y) = x – y + xy on the closed…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x+ 8y + 12z on the elipse…

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Q: Find the maximum value of f(x, y) = 3ry(9 – 45x – 9y) over the triangle with vertices (0,0), (,0)…

A: Maximum value occurs at critical points or on the boundaries of the triangle.

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: 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 values of f(x, y)= xy on the quarter-disk D={(x,y)l x20, y20,…

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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 maximum and minimum outputs for the function f (x,y) = xy – y² on the portion of the disk…

A: The given function is f(x,y)=xy-y2    ....(1) Let g(x,y)=x2+y2-1=0    ....(2) h(x,y)=x+y-1=0…

Q: Let f(x, y) = x² - y² + 2y. Find the absolute maximum and minimum values of f on the region 4x2 + y²…

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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 absolute maximum and minimum values of f(x, y) = 3xy−6x−3y + 7 on the closed triangular…

A: Find out the absolute maximum and minimum values of  f(x,y)=3xy-6x-3y+7 for the maximum and minimum…

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 all point on the plane x+ yt z= 5 in the first octant at which f(x, y,z) xy'z' has a maximum…

A: We have to find all points on the plane x+y+z=5 in the first octant at which fx,y,z=xy2z2 has a…

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: Find the absolute maximum and minimum values of the function f(x,y)=e** (x² +2y³) on the set D,…

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Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

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 absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = x2 - y2 - 2x + 4y + 1…

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

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Q: find the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the…

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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: 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 absolute maximum and minimum of the function f(x, y) = 3y – 2x2 , constrained to the region…

A: f(x, y) = 3y – 2x2 , constrained to the region bounded by the parabola y=x2+x-1 and the line y=x.To…

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

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Q: Find absolute maximum and minimum values of the function f(x,y) = 4xy – x²y² – xy + 1 in the closed…

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Q: By minimizing the function ƒ(x, y, u, y) = (x - u)2 + (y - y)2 subject to the constraints y = x + 1…

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Q: Find an equation for the level surface of the function f(x,y,z) = Vx+ y - Inz through the given…

A: Solve the given

Q: Find the surfaces on which the function u = 2 (x2 + y²)/z is constar

A: Since u is a constant so, x2+y2z=4a , where a is an arbitrary constant.

Q: For x,y,z > 0, use the Lagrange Multiplier Method to find the minimum value of 1 1 1 + + x y Subject…

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

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

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Q: Consider the function f(x, y) = xª + y4 – x² – y? – 2xy. | | Determine the maximum and minimum…

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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: The function f(x, y) = x² + 4y2- 2x + 8y-1 has a local minimum at the point (-1, 1). Select one: O…

A: We will use first order derivative to find critical point.  If given point is critical point, then…

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.

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.