Let f(x, y) be a function whose partial derivatives exist and are continuous at a point (a, b). Which of the following statements are true? Select all that apply. The linearization of f at (a, b) is not unique. fæ(a, b) is the slope of the tangent line to the O cross-section y = b at the point (a, b, f(a, b)) fy(a, b) is the slope of the tangent line to the O cross-section y = b at the point (a, b, f(a, b)) O None of the above

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: f(x, y) = −5x – 9y, (-4,9), A=4i-3j A) - 13 B) 5 C) -47 N D) //

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Q: Let f(x, y) = 2x²y³ - 2xy. Locate where the relative extrema and saddle points of f occur, if any.

A: The given problem is to find the relative extrema and saddle points of the given function…

Q: 2 Let f(x,y) = x +y ². Which of the following is the minimum directional derivative of the function…

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Q: Let f(x, y, z) = x² + yz, g(x, y) = y³ + xy. Use the chain rule to find the derivative of the…

A: As you don't want handwritten answer, I have used LaTeX.

Q: b. Find the angles 0 (with respect to the positive x-axis) associated with the directions of maximum…

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Q: Find the directional derivative of the function at P in the direction of v. V2 f(x, y) = x³ – y³,…

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Q: Calculate the directional derivative of the function f(x.y.z)= In(xy+xz+yz) at (1, 1, 1) in the…

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Q: Find the derivative of f(x, y, z)=x²-xy² -z at the point p (1,1,0) in the direction of V=i-j+2k (it…

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Q: Consider the function f(r, y) = 212 + ry – 6ry + 5x +2. (a) Show that (1,3) is a stationary point of…

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Q: derivative of f(x, y, z) = x + z at P(6,5,-5) in the direction from P to Q(5,7, -4). NOTE: Enter the…

A: We can solve this as follows: