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

Q: find the gradient of the function and the maximum value of th directional derivative at the given…

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Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: Allow f(x, y) = xe^(xy), now find the maximum rate of change of f at the point (3, -1).

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Q: Find the maximum rate of change of fat the given point and the direction in which it occurs. f(x, y)…

A: Note: where △f(x,y) = ∂f∂x,∂f∂y

Q: Please find the gradient of f(x, y) = ln(x² + xy²) at (2, 1)

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Q: Find the indicated partial derivative. f(r, y, :) = e"vz*; fzyz fxyz(x, Y, z) =

A: Given: f(x,y,z)=exyz3 To find: fxyz=?   Required formulas: Power rule: ddxxn=nxn-1 Product rule:…

Q: Find the gradient of the function f(x, y, z) = yz², at the point (0, -1,–1) V f(0, –1, –1) =

A: fx, y, z=yz2 & the point is 0, -1, -1. Partially differentiating with respect to x, we get fxx,…

Q: Use the Chain Rule to evaluate the partial derivative at the point (u, v) = (0,5), where g(x, y) = x…

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Q: e) The maximum rate of change of f(x, y) at the point (x, y) = (1, 0) is

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Q: Find the gradient of the function g(x,y) = xy at the point (3, - 1). Then sketch the gradient…

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

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

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Q: Find the direction in which f (x, y, z) = z exy increases most rapidly at the point (0, 1, 2). What…

A: We have given f(x, y, z) = zexy and the point (0, 1, 2).

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

A: Given,

Q: F(X, y,z) = 2x -y? +z?

A: F(x,y,z)= 2x-y^2-z^2 at point (4,-4,2) df/dx= 2 df/dy=-2y df/dz= -2z

Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

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Q: Find the gradient of the function w = xy2z2,  and the maximum value of the directional derivative at…

A: Given function:    w=xy2z2

Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² I in the…

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Q: Find the direction in which f (x, y, z) = z e*Y increases most rapidly at the point (0, 1, 2). What…

A: Given Data: Function: fx, y, z=zexy Point: x, y, z=0, 1, 2   The gradient of the function is, ∇fx,…

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

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Q: Find the maximum rate of change of f(a, y, z) tan(6z + 4y + 2z) at the point (- 4, 3, - 6).

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Q: Find the gradient of the function f(x, y, z) = √(x2 + y2 + z2), and the maximum value of the…

A: The given function is fx,y,z=x2+y2+z2

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

A: The given function is: f(x,y)=8yx

Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² H in the…

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

A: The objective is to find the maximum rate of change of f at the given point and the direction in…

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

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

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

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

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

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Consider the function defined by 1 g(x, y) = cos (Tx Vy) + log3 (x – y) Calculate the instantaneous…

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Q: Find the maximum rate of change of f(z, y, z) = tan(6z + 2y + 3z) at the point ( – 1, 3, – 2).

A: We need to find maximum rate of change.

Q: Find the gradient of the functions below. a)f (x, y, z) = sin(xyz)

A: Here we will find out the required value.

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

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Q: Find the linear approximation to f(x, y, z) = at the point (3, -2, -2): f(x, y, z) Z

A: To find the linear approximation of the below function at the point 3,−2,−2. fx,y,z=xyz

Q: Find the gradient of f(x,y,z)=xy+yz+xz at point P(1,2,3).

A: As we know that the expression for the gradient is: ∇fx,y,z=i∂∂x+j∂∂y+k∂∂zfx,y,z Given:…

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

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

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

A: We have to solve

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

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Q: #2. Consider the function f (x, y,z) = xy+3xz² + 5y at the point (1,0, 2) (a) Find the direction in…

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Q: Find the direction of the maximum rate of increase of f(x,y, z) = y²sinxz² at the point (0,3, –1).…

A: Given the function f(x,y,z)=y2sin(xz2) And the point (0,3,-1)

Q: 4. Let f(x, y, z)= xy²z² - 2xyz a) Find the rate of change of f(x, y, z) at P(1, 1, -1) in the…

A: The gradient of a scalar function at any point describes the direction in which the scalar function…

Q: Find the maximum rate of change in f (x, y, z) = tan(r + 2y + 3z) at P = (-5,1,1).

A:

Q: Find the gradient of the function f(x, y) = (x + y)/(y + 1),and the maximum value of the directional…

A: Given: fx,y=x+yy+1 The gradient of fx,y can be calculated as, ∇fx,y=i^∂∂xfx,y+j^∂∂yfx,y Here,…

Q: Find the maximum rate of change of f(x, y) : = ye* at the point (0, 2).

A: Introduction: Let f(x,y) is the function of two variables x and y. then the maximum rate of change…

Q: (b) Find the partial derivative at point (u,v) = (-4,0) of w = In(xª + yß + zª),x = ue"sinu, y =…

A: Chain rule:  Suppose that  are differentiable functions of and  is a differentiable function of .…

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

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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…