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I agree with you on setting $$ D_\vec u f = 10$$ then solve backwards to find the $\vec u. $ or you could keep plugging a bunch of different numbers in to try to find a dot product vector that would equal 10, but I feel like it would be easier to work the problem backwards to find it.

I'm also getting a different answer for my gradient. I'm not very good a derivatives though so it could be why. But the partial derivative with respect to x should be $ y^3$ right? Since the derivative of x would be 1 then you leave the second part alone. Then since y is constant the first left alone times the second part would be 0. Which would make the partial derivative with respect to y be $3xy^2$ which plugging in $ \langle 2,1\rangle$ would be $\nabla f =\langle 1,6 \rangle $ if I'm thinking about that wrong could someone explain where my thought process went bad?