Find the stationary points of the function: f(x,y,z) = 2*y*z + 7*x*z - z + 5*x*y + y x = ? y = ? z = ?

Q: Find ∇f(x, y, z) for the function f(x, y, z) = x2 + y2 − 4z and find the direction of maximum…

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Q: What does it mean for a function of two variables, f (x, y),to be differentiable at a point (a, b)?

A: A function differentiable at a point has a derivative that is defined at that point. This is defined…

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: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: Find the linear approximation of the function f (x, y) = 2x – y+x?y - near the point (2,0). O 2x +…

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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: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: Consider the function F(x, y) = x + 3x2 - 6xy? +2y3, Find critical points (FoC). Identify these…

A: Given function  F(x,y)=x3+3x2-6xy2+2y3 a. Differentiating F partially w.r.t to x and y, we get…

Q: Find the domain of the function f(x,y)=arccos(x²+y²-49360). O {{x,v) E R² | x,y € R}. O {(x,y) € R²…

A: Consider the function fx,y=arccosx2+y2-49360. Here, the objective is to find the domain of the…

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 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 linear approximation of the function f (x, y, z) (3, 2, 6) and use it to approximate the…

A: Given that  f(x,y,z)=√(x^2+y^2+z^2) To find the linear approximation of f(x,y,z) and also find the…

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

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Q: Let y = f(x) be a derivable function implicitly defined by the equation x2 + y2 = 1 . Calculate y'.

A: The power rule of differentiation to differentiate a function of the form y=xn,is stated as…

Q: Find all stationary points of the function z = f(x, y) = 3x² – 6xy + 2y³.

A: To find stationary points of the function z=fx,y=3x2-6xy+2y3

Q: Write the function z = xy + x - y in the form F(x, y, z) = 0.

A: Given: z=xy+x-y for writing given function in the form of Fx,y,z=0 we need to do transportation of z…

Q: f(x, y) = x² – y²

A: f(x,y) = x2 - y2 Let us firstly find the first order partial derivatives of the given function.…

Q: Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use…

A: Given:      f(x,y) = √ (155 - 2x2 - 5y2 )     Point : ( 5 , 4 )  Now     Linear approximation f (…

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) = xe*Y. Find the maximum rate of change of f at the point (2, 1). хе

A: We will find the maximum rate of change.

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 6, Vf(4, 2) = eBook

A: A detailed solution is given below

Q: Find the direction at which the function f(x, y, z) increases fastest at (2, 0, 0) = x In(e' – xz)…

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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. f(x, y) = 2x + 4y2 + 1, (1, 5) Vf(1, 5) =

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Q: Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate…

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Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

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Q: Find the linear approximation of the function at the given point. f(x, y) = -4x²y³ at (-9,7) O A.…

A: In this question we have to find linear approximation of the given function.

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

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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: 11.2.4. f(x, y) = V]xy|.

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Q: Find the gradient of the function at the given point. g(x, y) 6xey/x, (1, 0)

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Q: Consider the function f(x, y) = 3x? + ry + 2y? Use the linearization of f(x, y) about (1, 1) to…

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Q: Consider the function: f(x,y) = 5xy - 7x² - y² + 3y, (a) Given that x = 6±0.6 and y=9±0.7, calculate…

A: As per the question we are given the following bivariate function : f(x,y) = 5xy - 7x2 - y2 + 3y And…

Q: Consider the function f(x, y) = Va+y+I x-1

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Q: Find the gradient of the curve y = a²xe-b*x at x = 1.

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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: Find the linearization of the function at the given point. f (x, y) = e sin y, 0, 7).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

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Q: Find the relative maximum and minimum values. f(x.y)=x +xy+y° 28y + 261

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Q: Find the partial derivative  let z= f(x,y) =(x+y)^8 a. 8(x+y) b. 8(x+y)^7 c. 8x(x+y)^7 d.…

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Q: Find and determine type of stationary point for f(x,y)= 2x² – 4.xy + y² +x+3y

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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: Consider the function f: R²R given by f(x, y) = ³ + ² + 2xy + y2-y. Find and classify all stationary…

A: Here is the solution:

Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

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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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Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-3,0, (0,…

A: Sorry I cannot recognize your given points. So I provide only methods of problem you can easily…

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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