Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it occurs.

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: Let f(x, y) = sin(x+ y²). Compute the rate of change in the direction of fastest decrease for f at…

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Q: The value of local acceleration in the x direction for flOW with all wrong u = 2(1 + t) is given by…

A: Given that  u=2(1+t)  To find the local acceleration in the x direction of flow

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 f(x,y)= e^x^2 at (3,0) and the direction in which it occurs.

A: GIVEN DATA : Function fx,y=ex2        TO FIND : Maximum rate of change at 3,0 and the direction  The…

Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

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Q: Find the maximum rate of change of the function f(x, y) 4y at the point (5,1)

A: Given f(x, y) at (5, 1)  We have to find find the maximum rate of f(x, y) at (5, 1) by using the…

Q: Find the maximum rate of change of the function f(x, y) : 4y4 at the point (1,3)

A: We will solve the problem

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 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: find the total derivative of z = f(x,y) = 2x+xy-y2 where x=g(y)=3y2

A: Given function: z=2x+xy-y2 where x=3y2 Putting the value of x in z , we get…

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: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

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

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Q: Find the third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

Q: 2. Let f(r,y) = n: Find the maximum rate of change of f(r, y) at the point (4, 1) and the direction…

A: Given the given function is fx,y=xx-y and the point is 4,1. Apply formula for the maximum rate of…

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

A: Given that: fx,y=2sinxy,               0  ,  5

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: 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 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: (a) Find the derivative of ƒ(x, y, z) = x3 - xy2 - z at P0(1, 1, 0) in the direction of v = 2i - 3j…

A: We have given function fx,y,z=x3-xy2-z, point P01,1,0 and vector v=2i^-3j^+6k^

Q: Find in what directions does flx, y, z) = 4x 2– 9z + 2z In(y) increase and decrease most rapidly at…

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Q: (2) Let f(x, y, z) = xy + yz + x²z². What is the maximum rate of change of f at (1,2, 3)?

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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 maxcimum rate of change of f at the given point and the direction in which it occurs. F(x,…

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Q: Let f (x,y,z) = xln(yz). Find the maximum rate of change of f at the point (1,2,;) and the direction…

A: Suppose f  is multivariable function as f=fx,y,z then gradient vector is a vector that is composed…

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: 4y4 at the Find the maximum rate of change of the function f(x, y) point (5,1)

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Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: What is the average rate of change of y with respect to over the interval [-1, 2] for the function y…

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Q: The maximum rate of change at a point on a function f(x,y,z) is да ylgr

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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 maximum rate of change of the function f(x, y) 3y5 x at the point (3,4)

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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: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)?

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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 linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 5z) at the point (- 1, 1, 2).

A: We have to find

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

A:

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

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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(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: Find the maximum rate of change of f(r,y) = sin(x + y) at the point (1,-1) and the direction at…

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Q: Find the maximum rate of change of the function f(x, y) 4y5 at the point (5,4)

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Q: Find the maximum rate of change of f(x, y, z) = tan(7x + 3y + 6z) at the point (4, – 5, 2).

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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: SOLUTION-