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. ( 1,2, 4 ) and (1, -2, 4) O b.( 1, 4, 6 ) O c. ( 1, -3, -6 ) O d. (-1, -3, 6 ) and ( 1, -3, 6 ) O e. ( 1, 3, 6 ) and ( -1, -3, -6 )

Q: 1-Find the gradient of (1) f (x,y)= In(x²+y²) (1,1)

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Q: Question 2 Given the function of two variables f(x,y) = 8x2+6xy +4y2+5 a) Find the gradient vector…

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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. w = x tan(y + z), (6, 15, –13)

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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: 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) = 5x + 2y2 + 4, (4, 2) %3D Vf(4, 2) =

A: If f is a function of x and y then gradient of f is given by ∇f=∂f∂xi^+∂f∂yj^So, ∇fa,b is given by…

Q: Find the linearization L(x,y) of the function at each point. f(x у) — х2 + у2 +1 а. (1,1) b. (4,2)…

A: Solve the given function

Q: The present problem focuses on the function v defined by Equation (1): 1 1 v(x, y) = x² + y?+ (1)…

A: Given,  v(x,y)=x2+y2+1(x-12)2+y2+1(x+12)2+y2 To find the stationary points while x=0.

Q: assume thatf (2, 3) = 8, fx (2, 3) = 5, fy (2, 3) = 7 Which of (a)–(b) is the linearization of f at…

A: Consider the given: f2,3=8fx2,3=5,fy2,3=7,

Q: If f(x.y.z) x²yz + y2xz + z2xy, then the gradient of f at (-1,-1,-1) is: A) (4,4,4) E) (2,2,0) B)…

A: Given that, fx,y,z=x2yz+y2xz+z2xy The gradient of f(x, y , z) is ∂f∂x, ∂f∂y, ∂f∂z The gradient of…

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = x2 + y2 + z2…

A: given that a function f(x,y,z)=x2+y2+z2 we need to find the linearizations of f(x,y,z) at (1,1,1).…

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: Which of the following functions V(y1; Y2) is a Lyapunov function for the dynamical system y1 =…

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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: Solve the following

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

A: ∇f = &lt;∂f/dx, df/dy&gt; ∂f/dx = 4 df/dy = 10 y

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

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Q: Let f(x, y) = 2x² + 5xy + 2y² + 5x – 5y + 2. Find the linearization L(x, y) of f(r, y) at the point…

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Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

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 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: Suppose S = {r,u, d} is a set of linearly independent vectors. If x = 2r + 2u + 2d, determine…

A: Given :  S = {r, u, d} is linearly independent set of vectors  and  x = 2r+2u+2d. To find :  We have…

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: 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 linearizations L(x, y, z) of the function at the given points. ƒ(x, y, z) = x2 + y2 + z2 at…

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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: Which of the following functions V(y1, Y2) is a Lyapunov function for the dynamical system y1 =…

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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: In Exercises 1-6 find the gradient of ƒ at the indicated point. 1 f(x, y) = /x² + y² ; P(-4, 3) %3D

A: Solution Given f(x,y)=x2+y2 ; P(-4,3)we need to find the gradient of f at the indicated point.

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: Let f(x, y, z) = 6æ² + æy + yz + 7z?. Fina the linearization L(x, y, z) of f(x, Y, z) at the point…

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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. In(x² – y) – 3, (3, 8) z = 1 Vz(3, 8) = 2i

A: I have checked the work. Calculation is correct.

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

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Q: e S = {r, u, d} is a set of linearly independent vectors. d, determine whether T = {r, u, x} is a…

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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: Given f(x, y, z) = xy z.Which of the following is the gradient vector of f %3D at the point…

A: The given function is f(x, y, z)=xy2z3 at the point (1,-1,-1). The gradient of a function f(x, y, z)…

Q: J f ds if Evaluate Of(x, y, z)=x+y, and C is the combinations of lines connecting adjacently the…

A: As per company guidelines we are allowed to solve one question at a time so i am solving first one…

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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