Which of the following is (are) true about f(x, y)? The directional derivative at (0, 0) in the direction of a unit vector u = (u₁, U₂) is 1. f(x, y) = ²y, if (x, y) = (0,0) + 0, otherwise The directional derivative at (0, 0) in the direction of a unit vector u = (u₁, U₂) is where u₁ is non-zero. u²2 ալ " Amongst all directional derivatives at (0, 0), the maximum occurs in the direction of the vector (5, 5). There is no plane which contains all the tangent lines at (0, 0) and hence the tangent plane at (0, 0) does not exist.

Q: 5. Find the directional derivative of f(x, y) = xy – y at the point (1, 2) along the unit vector…

A: The given function is: f(x,y)=xy-y2 Given point is: P = (1, 2) Direction vector is: v=3, 4

Q: Consider the function Question 1 x f(x, y) = -y ln x + x lny + y a) Find the directional derivative…

A: Hints: The given function is f(x,y)=-ylnx+xlny+xy The direction vector of a is a⇀a. Therefore the…

Q: Let h(x, y) be a differentiable function and let (xo, yo) be a point in the domain of h. Also, let u…

A:

Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

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Q: Consider the function f(x,y) = 3- a. Fill in the table with the values of the directional derivative…

A: Here to find the directional derivative at (a, b) of fin(x, y) the direction of unit vector u, v and…

Q: (a) Find the directional derivative of z = x²y at (5,5) in the direction of π/2 with the positive…

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Q: c) Find the directional derivative of f(x,y) = 10 – 3x2 + at P(2,–3) in the direction of the vector…

A:

Q: Find the directional derivative of f (x, y, z) = 2z²x + y° at the point (2, 1, 2) in the direction…

A: Here, f(x, y, z) is given we have to find directional derivative of f(x, y, z) at point (2, 1,2) in…

Q: Find the directional derivative at (1, 1) if Vƒ(1, 1) = (3,−1) in the direction of the unit vector u…

A: Use the formula of directional derivative.

Q: 2. Consider the function f(x, y) = a) Find the directional derivative of f in the direction of the…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

Q: rative of the f he unit vecto p, then Ja + B|

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Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

Q: Find the directional derivative of the function f(x, y,z) =x-y+2z at the point P(1,2,3) in the…

A: Note:- Let a function f(x, y, z), then Direction Derivative of the function f at point P in…