Mathematics, 21.10.2020 16:01, markell42

Find the directions in which the function increases and decreases most rapidly at P0. Then find the derivatives of the function in those directions. F(x, y) = x^2 + xy + y^2, P0(-2,3)
The direction in which the given function f(x, y) = x^2 + xy + y^2 increases most rapidly at P0( -2,3) is u = i + _j.
The direction in which the given function f(x, y) = x^2 + xy + y^2 decreases most rapidly at P0( -2,3) is -u = i + _j.
The derivative of the given function f(x, y) = x^2 + xy + y^2 in the direction in which the function increases most rapidly at P0( -2,3) is D uf = .
The derivative of the given function f(x, y) = x^2 + xy + y^2 in the direction in which the function decreases most rapidly at P0( -2,3) is D -uf = .

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Find the directions in which the function increases and decreases most rapidly at P0. Then find the...