Le tf(x, y .z) be a function with the gradient vector < 2, 6, 12 >. What are the extreme points of f with constraint x² + y2 +z2 = 46 ? O a. ( 1, -3, -6 ) O b. ( 1, 3, 6) and (-1, -3, -6 ) OC. (1, 4, 6 ) Od. (-1, -3, 6 ) and ( 1, -3, 6) O e. ( 1,2, 4 ) and (1, -2, 4)

Q: Let f (x. y , z) be a function with gradient vector . What is the point of extreme value of f with…

A: To find: The extreme value of f with the constraints x+y+z=4. Given information: The function f(x,…

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (1, 5) Vf(1, 5) =

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Q: 7. Given the function f(x, y, z) = x² + y² + z² + xy + xz, find the gradient at P(1,2,1).

A: Must Know : Gradient function is given by ∇f=∂f∂xi+∂f∂yj+∂f∂zkGiven : f(x,y,z)=x2+y2+z2+xy+xz…

Q: Let f (x, y, z) be a function with gradient vector . What is the point of extreme value of f with…

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Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = √(x2 + y2 +…

A: Given: Function f(x,y,z) as follows: and a point (1,2,2) To find: Linearization L(x,y,z) of the…

Q: QUESTION 9 Letf(x yz) be a function with the gradient vector . What are the extreme points off with…

A: Given: ∇f=&lt;2, 6, 12&gt;g=x2+y2+z2=46  We solve it by method of Lagrange multipliers ∇f=λ∇gg=k

Q: Le tf(x, y.z) be a function with the gradient vector . What are the extreme points of f with…

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 4, (1, 2) Vf(1, 2) =

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Q: Find the gradient of the function at the given point f(x, y) = 5x + 4y² + 1, (1,4) Vf(1, 4) =

A: Solution of given question is written in below steps.

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y² +6, (3, 1) Vf(3, 1) =

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Q: Find the gradient of the function at the given point. f(x, y) = 3x + 5y2 + 8, (2, 1) Vf(2, 1) =

A: We have given function  fx,y=3x+5y2+8 fx=∂fx,y∂x fx=3∂x∂x+5∂y2∂x+∂8∂x fx=3+0+0 fx=3  .........(i)…

Q: Find the gradient of f(x,y.z)= (x2 + y2 + z2) - 1/2 + In (xyz) at the point (1,- 2, - 2) %3D Vf (1.…

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Q: The gradient vector of the function f(x, y, z) = ln(yz) - x² is: Select one: ○ (−2x,, 1) O None of…

A: To find the gradient vector of the functionf(x, y, z) = ln(yx)-x2

Q: Let f (x, y, z) be a function with gradient vector . What is the point of extreme value of f with…

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Q: Compute the gradient of the function at the given point. f (x, y, z) = In(x² + 7y - 3z²), (7,7, 7)…

A: option (b) is correct

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (4, 1) Vf(4, 1) =

A: f(x,y)=5x+3y2+5 fx(x,y,z)=5fy(x,y,z)=3(2y)=6y∇f =fx(x,y,z) i +fy(x,y,z) j

Q: Find the gradient of the function at the given point. In(x² – y) – 6, (2, 3) z = Vz(2, 3) =

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Q: Find the gradient of the function at the given point. In(x² – y) – 6, (3, 8) z = Vz(3, 8) =

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 5y + 4, (3, 2) %3D Vf(3, 2) =

A: We will solve the problem.

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 1, (1, 5) Vf(1, 5) =

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Q: Find the gradient of f(x,y,z) = (x² + y² +z²) Vf|(1,2,2) = Oi+Dj+Ok (Type integers or simplified…

A: ∇f(x,y,z) = ∂∂xi+∂∂yj+∂∂zkf(x,y,z)

Q: The gradient vector of the function f defined by f(x,y)= In(1+7x² +5y²) is equal to Select one: O…

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Q: QUESTION 9 Le tf(x, y.z) be a function with the gradient vector . What are the extreme points of f…

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Q: The gradient vector of the function f(x, y) = ln(xy) — x³ at the point (-1, 1) is (-1,-2). Select…

A: This question is based on gradient of function at a point.

Q: The function f whose gradient vector is vf(x,y) = (xIn(v + 7), 7x + y + 7> has two critical points…

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Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: Le tf ( x, y ,z ) be a function with the gradient vector . What are the extreme points of f with…

A: Let gx, y, z=x2+y2+z2 The gradient value of f and g are                  ∇fx, y, z=2, 6, 12∇gx, y,…

Q: Find the gradient of f(x,y,z) = (x² + y² +z²) ¯ - 1/2 Vf(-21.-2)=(1+Dj+k (Type integers or…

A: topic - gradient of a function

Q: Find the gradient of z = (7x + 4y)e. Assume the variables are restricted to the domain on which the…

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Q: Find the gradient of the function at the given point. w = 5x²y-7yz+z², (1, 1, -2) O 15i+ 26j+ 11k O…

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Q: - 1/2 Find the gradient of f(x,y,z) = (x² + y² + z²) 23 23 26 Vf|(- i+ - (-2,2,-1) 54 |j+ 54 27…

A: The function is f(x, y, z)=(x2+y2+z2-1/2+ln(xyz)  The point is (-2, 2, -1)

Q: QUESTION 9 Letf(x, y,z) be a function with the gradient vector . What are the extreme points of f…

A: We have to determine the extreme points on the given surface .

Q: Let f (x, y , z) be a function with gradient vector . What is the point of extreme value of f with…

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Q: If L(x, y) is the local linear approximation of f(x, g(2, 1)= 4, g,(2, 1)=4 and g,(2, 1)=6, then L O…

A: Use formula of linear approximation

Q: Let f (x, y, z) be a function with gradient vector . What is the point of extreme value of f with…

A: Given, f(x, y, z) be a function with gradient vector &lt;2x, 4y, 4z&gt;. i.e. ∇fx,y,z=2x,4y,4z…

Q: Find the gradient of the function w = x tan( y + z), at the given point (4, 3, −1)

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Q: Let A e Rmxn,x, b € R, Q(x) = || Ax – b||3. (a) Find the gradient of Q(x). (b) When there is a…

A: Given : A∈ℝm×n , x, b∈ℝ, Qx=Ax-b22 To find : (a) gradient of Qx (b) a unique stationary point for Qx…

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y² + 4, (3, 4) Vf(3, 4) =

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Q: Letf(x, y,z) be a function with the gradient vector . What are the extreme points of f with…

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Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vfl(-12,-2)=i+j+k (Type integers or simplified…

A: Given

Q: The gradient vector of the function f(x, y) = 2+ Ty at the point (1, 1) is %3D Select one: O True O…

A: The gradient vector of function f is given by: ∇f=∂f∂x,∂f∂y Here, ∂f∂x=12xyy=y2xy∂f∂x=12xyx=x2xy

Q: -1/2 Find the gradient of f(x,y,z) = (x² + y² +2²) −1/² + In (xyz) at the point (1,2,2). Vfl…

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Q: 1. Consider the function f (x, y, z) = 2°y – xyzešzy Compute the gradient of f.

A: Let's find.

Q: Find the gradient of the function In(x² − y) – 1, X Vz(2, 3) = Z at the given point. (2, 3)

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Q: Find the gradient of the function at the given point. In(x² - y) - 9, (2, 3) = Z Vz(2, 3) =

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Q: Le tf ( x, y ,z ) be a function with the gradient vector . What are the extreme points of f with…

A: This is a problem of function of several variable We have to find the extreme point in three…

Q: Letf(x, y.z) be a function with the gradient vector . What are the extreme points of f with…

A: The given constraint can be written in the form of g(x,y,z)=0 as shown below:…

Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vfl (1,2,2)=(i+₁+O (Type integers or simplified…

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y² + 4, (1, 2) Vf(1, 2) =

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