Is there a direction u in which the rate of change of the temperature function T(x, y, z) = 2xy - yz (temperature in degrees Celsius, distance in feet) at P(1, -1, 1) is -3°C/ft? Give reasons for your answer.

Q: The directional derivative of f(z, y,2) = r'y- v': at the point (3,2,1), in the direction of the…

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Q: 3) Find the maximum rate of change of f at the given point P and the direction in which it occurs.…

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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: Let z = Vx+ 3y. Then: The rate of change in z at (2, 1) as we change x but hold y fixed is The rate…

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A: Note: where △f(x,y) = ∂f∂x,∂f∂y

Q: The temperature at any point (x, y) in a steel plate is T = 900 -0.7x² - 1.1y2, where x and y are…

A: topic- partial differentiation

Q: (a) Find the derivative of f(x, y, z) =x²- xy²- z at Po(5, 1, 0) in the direction of v=2i-3j+ 24k.…

A: Given: f(x, y, z) = x2 - xy2 - z, P0(5, 1, 0) and v=2i - 3j + 24k.

Q: The gradient of the tangent to the curve y=flx) at the point P(2, (2)) is given by A 12) – h f(2+k)…

A: To find the gradient of the tangent to the curve y=fx at the point P2, f2.

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

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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 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: 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: Is there a direction u in which the rate of change of ƒ(x, y) = x2 - 3xy + 4y2 at P(1, 2) equals 14?…

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Q: 2. Is there a direction u in which the rate of change of the temperature function T(x, y,z) = 2xy –…

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Q: Find the directional derivative of f(x, y) = cos(x) + y² at (T,2) in the direction of (3, –4).

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Q: Find the directional derivative of f(x, y) at P(5,0) in the %3D x + y direction of Q(3, –3). NOTE:…

A: Given- f(x,y)=20xx+y To find the directional vector of f(x, y) at P(5,0) in the direction of…

Q: Find the maximum rate of change of the the function 80 f(x, y, z) = 1+g² + 2y? + 3z² %3D at 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: (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: The temperature at a point (x,y) on a flat metal plate is given by T(x,y)=60/(1+x2 +y2 ), where T is…

A: Given,           The temperature at a point (x,y) on a flat metal plate is given by…

Q: Find the directional derivative of f(x, y, z) = 4xy + z at the point (5, –5, 3) in the direction of…

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Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),…

A: Given that      f(x,y,z)=ln(x2+3y2+9z2), P0(3,3,3), u=3i+4j Here we have to find the derivative of…

Q: The directional derivative of f(, y) = In(x² + y²) at the point P(1,5) in the direction v (3, 4) is…

A: We have to find the directional derivative of the function fx, y=lnx2+y2 at the point 1, 5 in the…

Q: 8. The temperature of the xy-plane is given by the function f(x, y) = x²y+e¬¤. (a) At the point…

A: The direction of maximum decrease of a scalar function f(x, y) is given by the negative of the…

Q: The temperature at any point (x, y) in a steel plate is T = 500o - 0.5x2 - 1.2y2, where x and y are…

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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, у)…

A: Given function and point is

Q: The directional derivative of f(x, V, 2)=y-vz at the point (2, 1,1), in the direction of the tangent…

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Q: Find the directional derivative of f(x, y, z) = 3æy + z2 at the point (5, 3, 5) in the direction of…

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Q: Find the derivative of the function at Po in the direction of A f(x,y,z) = 3 e* cos (yz), Po(0,0,0),…

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Q: Find the magnitude of the greatest rate of change of f(x, y, z) = (x2 + z2)3 at (1, 3, -2), and…

A: Consider the provided question,

Q: The temperature at point (x, y, z) is given by T(x,y, z) = xy + sin(yz). Find the direction from…

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Q: If f(x,y, z) = x²y cos(2ryz), find the rate of change in the function at the point (x, y, z) = (1,1,…

A: The gradient of the function is defined as ∇f=⟨fx,fy,fz⟩. The directional derivative in the…

Q: The rate of change of y is proportional to y. When t = 0, y = 2, and when t = 2, y = 4. What is the…

A: Given that rate of change of y is proportional to y that is, dydt=ky        ...(1)

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: The temperature at any point (x, y) in a steel plate is T = 500 - 0.6x2 - 1.2y2, where x and y are…

A: Partial differentiation with respect to x. Treat every other variable as a constant.

Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = x2 + 2y2 – 3z?, Po(1,…

A: We can solve this as follows:

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: The directional derivative of 2e" cos y at f(x, y) = -2e* cos y at (0, 7) in the direction of v =…

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Q: Find the derivative of the function at P.(0,0,0) in the direction of B. f(x, y, z) = 3e* cos yz,…

A: Directional derivative of the function.

Q: 3x The directional derivative of f(x,y,z)=ln at the point P (2,0,-1) in the direction 1+yz z² from P…

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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: Is there a direction u in which the rate of change of the temperature function T(x, y, z) = 2xy - yz…

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Q: Find the derivative of the function at P,(0,0,0) in the direction of B. f(x, y,z) = 3e* cos yz,…

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

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