The maximum directional derivative of a function is given by the magnitude of the gradient vector. Then the maximum directional derivative of the function f(x, y) = x In y + x²y? at point (-1, 1) is given by А. -21 +j В. 15(-2î + j) С. 1 D. Е. 15

Q: 4. Find the directional derivative of f in the direction of vector v at point (1,3) such that v =…

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Q: Sketch the gradient vector Vf (4,6) for the function f whose level curves are shown. Explain how you…

A: Given the level curves of a function f. By observing the sketch of the level curves, we need to…

Q: Find the gradient of the function at the given point. z=y/x^2+y^2   (2, 2) Find the maximum value of…

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Q: a. What is the gradient at the point (4,0,1)?

A: Consider the given function fx,y,z=x2+y2+2z2+3.  The gradient of a function is given by,…

Q: If the gradient of f(x, y, z) at (1, 2, 3) is 2i – 2j +k, then the maximum value for a directional…

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Q: If f(x, y, z) = 4zy", then the gradient at the point (5, 4, 5) is V f(5, 4, 5) =

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) : x2 + y2 + z? (7,…

A: Formula for the directional derivative of the function f(x,y,z) is: ∇f = fxi +fyj +fzk Where…

Q: Find the gradient of /x, y. 2) eand the largest value of the directional derivative of fox. y. zi…

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Q: 2. Find the gradient vector at the indicated point f(x, у, 2) 3 ху — In (2),. (2, -2,2)

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Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) 3 x2 + y2 + z2 (7,…

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Q: Find the Directional derivative of the function f(x,y,z) = /x² + y² + z² from point (1,2, –2) in the…

A: The objective is to compute the directional derivative of the function fx,y,z=x2+y2+z2 from point…

Q: Prove that the vector given by (sin ysinh x + cos ycosh x) i + (cos y cosh x- sin ysinh x) j is a…

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Q: Find the gradient of the function at the given point. y Ri (2, 2) x²+ y2' Vf(2, 2) = %3D Find the…

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Q: Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables. 1) Find the gradient of…

A: Explanation of the answer is as follows

Q: Let f(x,y,z) = x ^3+2yz-z^2 What is the steepest directional slope at the point (1,1,1)

A: Given function is  fx,y,z=x3+2yz-z2

Q: Find the gradient of the function at the given point. Function Point (7,4) f(x, y) = Vf(7, 4) = x +…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z² (4,…

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Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² y2 + z2 (3, 5,…

A: To find the gradient of the function at the point given

Q: Find the gradient of the function at the given point. Function Point f(x, y, z)=√√√x² + y² + z² (8,…

A: Our Aim is to find the gradient of the function at the given pointwhere Function is…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = x² + y² + z² (8,…

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Q: Sketch the gradient vector ∇f (4, 6) for the function f whose level curves are shown. Explain how…

A: To draw the gradient vector at a point, determine the direction and the length of the vector. The…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = x² + y2 + z2 (2,…

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Q: The table shows experimental valucs of two variables x and y. 0.1 0.5 1 1.5 2 y -5.95 1.63 0.83 0.61…

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Q: (a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the…

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Q: If f(x, y) = xy, find the gradient vector Vf(7, 5) and use it to find the tangent line to the level…

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Q: Find a vector equation for the tangent line to the curve of intersection of the cylinders x2+y2=25…

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Q: Find the gradient of the function at the given point. In(x - y)- 4, (3, 8) Z = Vz(3, 8) =

A: The objective is to find the gradient function at the given point.

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y2 + z² (2,…

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Q: If f(x,y) = ln(xy) + x^2y^2, how do I calculate the second directional derivative of f in the…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) 2, Vw(10, 5, -2)…

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Q: Find the gradient of the function at the given point. Function Point (3, 7, 2) f(x, y, z)=√√√√x² +…

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Q: Find the gradient of the function at the given point. Function Point x + 2y y + 1 f(x, y) = (1, 2)…

A: We have to find

Q: Find the directional derivative of F(x,y,z)=(xy^2)lnz at (1,2,e) in the direction of

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Q: Find the gradient of the function at the given point. Function g(x, y) = ye-* Vg(0,4)= Point (0,4)…

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Q: Find the directional derivative of F(x,y,z)=x3y+4y2z+3xz3 at the point (3,-1,2)   in the direction…

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Q: 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1, -1). 2. Find the…

A: Given :fx,y,z=lnxy-zx2

Q: 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1,-1). 2. Find the…

A: The given function is f(x,y,z)=ln(xy)-zx2 We have to find the Gradient of the f(x,y,z)=ln(xy)-zx2 at…

Q: Find the directional derivative of the function: f(x, y) = ez² + 4y at the point (0, 0) in the…

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Q: Find the gradient of the function at the given point. Function g(x, y) = ye-x Vg(0, 9) = Point (0,9)…

A: Given function: g(x,y)=ye-x

Q: determine the gradient and equationof the tangent to the curver f(x,y) = 0 in the point (a,b) for…

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Q: Eavluate the gradient vector at the given point. a) f(x,y) = cos2(πxy) at (1,-1) b) f(x,y,z) = xeyz…

A: a) Given function is

Q: Find the gradient of the function at the given point. z = x?y, (7, 1) Vz(7, 1) = Find the maximum…

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Q: Find the gradient of the function at the given point. Function f(x, y) = x² Point (4,4) Vf(4,4) = x²…

A: In this question we have to find the gradient of the function. Note: As per our policy we can solve…

Q: Use Green's theorem to evaluate fxydx+ x3y3dy where C is a triangle with vertices (0,0), C (1, 0)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the gradient of /(x, y. 2) eand the largest value of the directional derivative of fox. y. z)…

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Q: Vhat is the gradient of g(x.y) = ye* and its maximum value of its directional derivative at P(0, 5)?…

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Q: in Exercises 29–38, find the gradient of the function and the maximum value of the directional…

A: form given curve equation we can find maximum rate of change at given point by using gradient of…

Q: Find the gradient of the function at the given point. Function Point (8,4) f(x, y) Vf(8, 4) = = = x…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y² + z² (5,…

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