Find the linear approximation of the function at the give f(x.y) = 3x y at (- 6,9) O A. L(x,y) = - 26,244x + 26,244y -314,928 O B. L(x.y) = - 26,244x- 4,374y - 314,928 OC. L(x.y) = 4,374x+ 26,244y - 314,928 O D. L(x.y) = 4,374x-4,374y- 314,928

Q: Find the second-order partial derivative fxx ( x , y ) of the function f ( x , y ) = x 6y 4 -…

A: Given f(x,y)=x6y4-2x7y8+17x-y

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: Find the gradient of the function at the given point.

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Q: ,2 For function f (x, y) x2+1 Evaluate the gradient at the point (1,2)

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Q: Find the gradient of the function at the given point. In(x2 - Y) - 9, (3, 8) Vz(3, 8) =

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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 maximum rate of change of the function f(x, y, z) = xy + yz - xz at the point P,(1, -3, 4).

A: As per our guidelines we are supposed to answer only one question.

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) =

A:

Q: Find the maximum rate of change of the following function at the given point. f(x, y, z) = x² + 5xz…

A: To Determine: find the maximum rate of change of the following function at the given point . Given:…

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

A: To find out the gradient of the function at the given point..

Q: Find the partial derivative of f(x, y) 8x - 2xy2 + y3 with respect to x at the point (2, 1, 61).

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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: Find the gradient of f(x, y) = y ln x + xy2 at the point (1, 2).

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Q: Find the location (x, y) of the minimum of the function: f (x,y)=3x² – 3xr+5+1.5xy +5y² – 4y…

A: Given : function          fx, y=3x2-3x+5+1.5xy+5y2-4y To find : location x, y of the minimum of the…

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

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Q: 2. Find the gradient of the function f(r.y) In(r y²) at the point( 1, 1).

A:

Q: Find the partial derivative of fy for the function 3 f (1, y) = (3x² +y²)* 6 (3æ² + y°)? 32 (3x² +…

A: To find: The partial derivative fy of fx,y=3x2+y23. Given: The function is fx,y=3x2+y23. Concept…

Q: Find the gradient of a normal line to the parabola y=x^2+5x-9 at the point (1,1)

A: In this question, the concept of slope is applied. Slope A line's slope or gradient is a number that…

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 8,    (2, 1) ∇f(2, 1) =

A: We have to find the gradient of the function  f(x, y) = 2x+4y2+8  at the point (2, 1).

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs…

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: Find the Partial derivative of f with respect to y for * 2. y² f (x, y) = x + y

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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: Compute the partial derivative fa(, 4, 2) of the function f(2,4, 2) = yz' + 2 – 2 vy + * +2 y. O…

A:

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

A: Given equation - f(x,y) = 3x+5y2+1We can write it as - y = 3x+5y2+1Gradient is given by , dydxNow…

Q: Find the gradient of the function at the given point. In(x2 – y) – 9, (3, 8) z = Vz(3, 8) =

A: use partial derivative for finding the gradient.

Q: The gradient of f(x, y) xy at (x, y) = (– 1, 1) is

A:

Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

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Q: Find the gradient of the function at the given point. In(x - y)- 4, (3, 8) Z = Vz(3, 8) =

A: The objective is to find the gradient function at the given point.

Q: w = 3x² – 5y² + 2z², (1,1, –2)

A:

Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…

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

A: The given function,   z=lnx2-yx-3, at the point 3,8

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: The gradient of f(x, y) = xy at (x, y) = (3, 1) is

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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: First, compute the gradient of the function p(x,y)= 12- 2x-y Then evaluate it at the point (- 1,2).

A: We need to find partial derivatives with respect to x and y to find gradient

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

A: This is a problem related to derivation. Please follow the procedure given below for solution.

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

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 2y + 3z) at the point (−9, 6, 2) and the…

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Q: Find the partial derivative of the function with respect to each of the variables f(x.y) =…

A: Given function is fx,y=100x0.64y0.36 find the partial derivative of the function with respect to…

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

A:

Q: Find the gradient of the function g(x, y) = 2xey/x , at the given point (2, 0)

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Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

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

A: To find the gradient of the function at the given point.

Q: Find the gradient for the curve defined by y + xy = 3 at the point (1,2)

A: Gradient to given curve

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

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