SHOW WORK Find all the points at which the direction of fastest change of the fu

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Find all the points at which the direction of fastest change of the function f(x, y) = x2 + y2 - 10x - 16y is i + j. The direction in which the maximum rate of change of f(x, y) occurs at a point (a, b) is given by the vector nablaf (a, b). For f(x, y) = x2 + y2 - 10x - 16y, we have We need to find all points (x, y) for which (2x - 10)i + (2y - 16)j is parallel to i + j. So we must solve (2x - 10)i + (2y - 16)j = k[i+ j]. This means that k = 2x - 10 and k = 2y - 16. Equating these gives us y = .

Explanation / Answer

I'd assume you just set the ks equal to eachother and solve for y? meaning that youd get

2x-10=2y-16

factoring that gives us 2y=2x+6

which gives us y=x+3

so i'd say go with that

any questions or problems, just ask :)

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