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A: Applications of derivatives
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A: Since solve the first question for you. If youwant any specific question to be solved then please…
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Q: EXERCISE 2 Consider f(x, y) = 3x² – 4y² and = = cos T î + sin 7 ĵ. Use the Theorem above to find the…
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A: Dot product of A.B is ad+be+cf where A=<a,b,c> and B=<d,e,f>.
Let f ( x , y ) = 2 x − y + x2 + y4.
Which (unit) direction
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- Suppose that f(x, y) = x³y². Find the directional derivative of f(x, y) in the direction of (-3, 1) at the point (-2,2). Note that the direction is not a unit vector.From the point (2,2), find the directions in which the directional derivative of f(x,y)=x2 +xy3 takes the value of 12.2. Find the directional derivative of 9 = yx? +x?z + 3xyz in the direction of vector n = Î + 2ŷ -? .
- Consider the function defined by f(x,y) = 4xy - 2x2. Evaluate the directional derivative of f at point(1,-1) in direction of the vector which subtends an angle of pi/6 with the positive x-axis.Consider the function f(x, y) = 4x² + 4y². π. Find the the directional derivative of f at the point (-3, 3) in the direction given by the angle = 름 Find the vector which describes the direction in which f is increasing most rapidly at (-3, 3).Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction (15/17, 8/17). Be sure to use a unit vector for the direction vector.
- Find the directions in which the directional derivative of f(x, y) = x² + xy³ at the point (3, 1) has the value 2.Let v = = (3,4, 12) . Find the directional derivative of f(x,y, z) = x – y² +3z³ in the direction of v.Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) =8xy2, (5,-7) maximum rate of change direction vector
- Find the gradient of the function w = xy2z2, and the maximum value of the directional derivative at the point (2, 1, 1).Let f(x, y) = xeY, P = (2, -1), and v = (2, 3). Calculate the directional derivative in the direction of v.Calculate the directional derivative of f(x, y) = xy in the direction of v = -2i+2j at the point P = (2, 2). Remember to normalize the direction vector. Duf(2, 2) =