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
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Q: a. What is the gradient at the point (4,0,1)?
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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…
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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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A: Explanation of the answer is as follows
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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…
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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…
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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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A: The objective is to find the gradient function at the given point.
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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. Function g(x, y) = ye-* Vg(0,4)= Point (0,4)…
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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…
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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…
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A: Hey, since there are multiple questions posted, we will answer first question. If you want any…
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Q: in Exercises 29–38, find the gradient of the function and the maximum value of the directional…
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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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- Find the gradient of the function at the given point. z=y/x^2+y^2 (2, 2) Find the maximum value of the directional derivative at the given point.Find the gradient of the function f(x, y, z) = xeyz, and the maximum value of the directional derivative at the point (2, 0, −4).A curve has Y= 4x + In (2x) for x>0, find the gradient of the curve at the point with the coordinates (1/2, 2)
- Find the gradient of pthe function and the maximum value of the directional derivative at the point (1;2)for g(x;y)=ln sqrt3 x^2+y^2Suppose that f(x,y)=(x^3)(y^2). The directional derivative of f(x,y) in the direction and at the point (x,y)=(2,-3) is?Suppose that f(x,y)=y. The directional derivative of f(x,y) in the direction of and at the point (x,y)=(2,5) is?
- A curve if define by that equation on picture, how to differentiate y for its gradient function?A curve C in the plane passes through (0,7) and (5,8). At each point on C, the tangent line has a slope that is proportional to the second coordinate of the point. What is the value of the constant of proportionality?Obtain the directional derivative of f (x, y) = 2root (x) -y ^ 3 at the point (1,3) in the direction towards the point (3,1), select the correct option.
- A curve has Y= 4x + In (2x) for x>0, find the x coordinate of the point on the curve where the gradient is 3The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) isUse implicit differentiation to help you find the value of the gradient for theequationx^2 - e^y = y(x - 2) + 8at the point (3; 0) and use linear approximation to estimate the value of ywhen x = 2.98.