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Social Scienceeh the directional derivative ofxy at the point (2, 1) has the value 2.29. Find all points at which the direction of fastest change of thefunction f(x, y)= x2 + y - 2x -4y is i +30. Near a buoy, the
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eh the directional derivative of xy at the point (2, 1) has the value 2. 29. Find all points at which the direction of fastest change of the function f(x, y)= x2 + y - 2x -4y is i + 30. Near a buoy, the
Expert Answer
Given function
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f(x, y) x2 - 2x 4y To find: all points at which the direction of the fastest change of function is i+j
Note:
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A scalar field fwill have its maximum rate of change in the direction of its gradient vector. Therefore, we find all points (x, y) where the gradient i.e. Vf(x, y) is parallel to i+j
Calculatin...
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Vf(x, y) (2y - 4)j = ki + kj, for some k> 0, giving 2x - 2 2y -4 (2x- 2)i + (2y 4)j Thus, (2x 2)i Or y x
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