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

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: 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: 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) Vf(4, 2) =

A: Topic = Functions

Q: Find the gradient of the function f(r, h) : 2rrh + r2 at the point (2, 3). Vf(2,3) =

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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 w = 2x²y - 4yz + z² at the point (1, 1, -2). ○ 2î+ 10j - sk Ⓒ41+…

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 10, (2, 3) Vf(2, 3) =

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

A: Given: fx,y=2x+3y2+2 ; Px,y=3,5   As we know that; The expression for the gradient vector.…

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…

A: Solve the following

Q: Find the gradient of the function f(r, h) = 2xrh + xr² at the point (2, 2). V f(2, 2) =

A: Given,   f(r,h)=2πrh+πr2

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: The gradient of the functiong(x, y, z) = In a In y In z at the point (2, 4, 3) is:

A: Given, g(x, y, z)=lnx lny lnz

Q: Compute the gradient of the function at the given point. f(x.y) = - 4x + 9y, (-8,-4) O A. - 256i -…

A: Solve the following

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: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: (2x, /, // ) (2x, -, -…

A: gradf =∇f =i∂∂x+j∂∂y+k∂∂zf .

Q: Find the gradient of the function f(x, y) = x²y+y³. Vf(x, y) = xî+ (x + 3y²) ĵ ○ ▼ f(x, y) = xyî +…

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Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: ○ (2x,-1,-1/2) (2x₂ O…

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Q: Find the gradient of the function w = 2x²y – 4yz + a at the point (1, 1, -2). O 2i+ 10j- 8k O 4i+…

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Q: Find the gradient vector and level curve of the following functions at the given point and show that…

A: Given,

Q: Calculate the gradient. h(x, у, 2) %3 хуz7 Vf =

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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: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) = %3D

A: To find the gradient of the function at the given point.fx, y=5x+2y2+4, 4, 2∇f4, 2=?

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: 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: 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 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: 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 gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2

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 at the given point. w = 6x2y-9yz+z2, (1, 1, -2) O 18i+ 33j+ 13k…

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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: 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 points P (x1, y1), Q(x2,y2) and R (x,y) are collinear. Use the gradient formula to show that…

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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: 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: 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: Compute the gradient for the function f (x, y) = 4x² – 9y at the point (10, -9) %3D

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Q: Find the linearization L(x, y, z) of the f (x, y, z) = 2/³ + y³ + z³ at the point (1, 2, 3 Answer:…

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Q: Consider the function f(x1, x2,x3) = xỉ + 2x3 + 2x3 + 2x1x2 + 2x2x3. Verify whether the vector d…

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