Let if (x, y, z) # (0,0, 0) if (x, y, z) = (0, 0, 0) xyz x²+y²+z² > f(x, y, z) = { 10, (a) Use the definition to find the directional derivative of the function f at (0,0, 0) in the direction (a, b, c), where a² + b² +c² = 1. (b) Use Lagrange Multipliers to find the maximal and minimal directional derivatives.

Q: A function z=f(x, y) is defined implicitly by the equation xy2 - x²z+yz² -z = 11 near point (2, -2,…

A: Given function is fx, y, z = xy2-x2z+yz2-z-11

Q: If 23 + 33 = d and -i + 53 = 6b, express i and y in terms of å and b.

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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: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

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Q: Find the directional derivative of the function at the point P(2,1) in the following direction:…

A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

Q: a) Find the directional derivative of the function f(x, y, z)= x² y2 (2z+1)2 at the point P:(1, - 1,…

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Q: Solve the following quadratic equation for all values of x in simplest form. (3x – 1)2 – 49 = –13 -

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Q: the directional d + 3y2 + 5z² at pa

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Q: 2 - What is the directional derivative of the function f(x,y,z) = x3 - 2xy +z at point Ao= (1,1,0)…

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Q: Example: Find the directional derivative of f(x, y, z)=x²-yz+xz² at P(1,-4, 3) in the direction from…

A: Directional derivative of f(x,y,z) in direction of some vector a is given by , Directional…