Find the minimum and maximum distances between the sphere r²+y²+z² = 9 and the point (2, 3, 4). Note: This can be done using second partials or LaGrange multipliers.

Q: 3. Find the maximum and minimum values of the function f (x, y, z) = x+ y + z on the ellipsoid x2 +…

A: Given we have given a function  f(x, y, z) = x+y+z we have to find the maximum and minimum value of…

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A:

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: To find the minimum distance from the given curve to the point using Lagrange multipliers method.…

Q: Find the point on the plane 3x + 2y + z = 6 closest to the origin. (Hint: Use Lagrange multipliers.)

A: Given plane is, 3x+2y+z=6, we need to find the point on this plane closest to the origin.

Q: Use the method of Lagrange multiplier to determine the maximum and minimum values of f(x, y) = x* +…

A: Local Maximum and Minimum by using lagranges Multiplayer.

Q: Use Lagrange multipliers to find the points on the cone z2 = x2 + y2 that are closest to (8, 2, 0)…

A: Given: Equation of the cone: z2 = x2 + y2 Given point: (8, 2, 0)   To find: The points on the cone…

Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

A:

Q: Find the maximum value that ƒ(x, y, z) = x2 + 2y - z2 can have on the line of intersection of the…

A: Given and planes are

Q: Find the minimum and maximum squared distance between the sphere x² + y² + z² = 9 and the point…

A: We have to find the minimum and maximum squared distances between the sphere x2+y2+z2=9 and the…

Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: 2. Use the method of Lagrange Multipliers to determine which point on the surface !++ = 1, æ, y, z >…

A: According to the Legrange multipliers method to find closest point on surface to origin, solve for…

Q: 3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid z = x²…

A: (3)Let (x,y,z) lies on parabolaThe distance d=x-32+y2+z2such that z=x2+4y2Lagrabge multiplier…

Q: 3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid z = x?…

A: Given,                               z=x2+4y2and the point (3, 0, 0).

Q: I need help finding the absolute maximum and minimum values of f on the set D.

A:

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: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

A: Use Lagrange multiplies we find heighest point on the curve ofintersection of the surface cone:…

Q: Use Lagrange's multiplier(s) to find the maximum and minimum for f(x, y, z) = x² + 2x + 2y2 + 3z2 on…

A:

Q: Find the ab solute moximurn ond minimum volueso the function triongulor region with vertices…

A: Differentiate the function fx,y=x2+y2-x-y+1 with respect to x and y, to obtain fx, fy, fxx, fyy and…

Q: 1/ Find maximum,minimum Z= x³y³-12x + 3y + 12. ,and saddle point of the surface

A: Use the method of Lagrange multipliers to find maxima minima of the given function as in next step.

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: Find the maximum value of f(x, y) = 11zy(9 – 99x – 9y) over the triangle with vertices (0, 0). (†,0)…

A: Given: The triangle vertices are (0,0),(111,0) and (0,1) f(x,y)=11xy(9-99x-9y)…

Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (2, 2, 0).

A:

Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: Find and classify all the critical points of the surface with its equation z = 32°y – y° + 3z – 3y²…

A: Given: z = 3x2y - y3 + 3x2 -3y2 + 2

Q: Find the maximum and minimum values of the function f(x,y, z) = x + y + z on the ellipsoid x² + 4y²…

A: To determine the maximum and minimum value of the function fx,y,z, subject to the constraint…

Q: Find the point on the plane 3x + 2y + z = 6 closest to the origin. Hint: Use Lagrange multipliers.

A: The given plane: 3x+2y+z=6 To find the point on the plane 3x+2y+z=6 closest to the origin. Solution:…

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: Integrate Xy ed २ over the triangular region with vertices: (0,0), ), (0,8) (0,16)

A:

Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

Q: Let P be the plane 2x + y – z = 2 and let Q(1,0,3) be a point. We want to find the minimum distance…

A:

Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: Find the minimum distance from the cone z = 2x2 + y2 to the point (-6, 4, 0).

A: To find the minimum distance first write distance function. Which is the square distance from  .

Q: Find minimum perpendecular distance between given paraboles. y = x2 + 1 y = x - x2

A: To find the minimum distance between 2 parabolas

Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

A:

Q: Find the extreme values of z on the surface 2x² + 3y2 + z2 - 12xy + 4xz = 35.(DO NOT USE LAGRANGE…

A: For the solution follow the next steps.

Q: Find the maximum value of f(x,y,z)=25x+3y+17z on the sphere x2+y2+z²=100

A:

Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

A:

Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

A:

Q: Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with…

A: Given,  Plane x + 3y + 4z = 9

Q: 5) Let R(x, y) = 3x² + y². Find the minimum value of R on the hyperbola xy 2.

A:

Q: Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).

A: To find the minimum distance

Q: The minimum value of f(x,y,z) = x^2 -2y + 2z^2 on the sphere x^2 + y^2 + z^2 =1 is ....?

A:

Q: 3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid 2= z +…

A:

Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

A: Given: Equation of cone is x2+y2-z2=0 and equation of plane is x+2z=4. To determine: The highest…

Q: Find the points on the cone z2 = x² + y2 that are closest to the point (8, 2, 0).

A: we have given the equation of cone z2=x2+y2 and the point (8,2,0)to…

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

Q: Find the absolute maximum and minimum values of f(x, y) Зху — Зх — бу + 9 %3D | on the closed…

A:

Q: 4) Let h(x, y) = 2x² + y² – 2x²y. Find the absolute minimum and maximum values of the surface on the…

A:

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…