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Calculus Level 4

A function $$F(x,y,z)$$ is known to have $$F(1,1,1) = 1, F(2,1,1) = 4, F(2,2,1) = 8, F(2,2,2) = 173$$. Find the sum of all the values of $$c$$ satisfying

$\displaystyle \left \lfloor {\nabla}_{5\textbf{i} + 9\textbf{j} + c\textbf{k}} F \right \rfloor = 16$

Note

Directional Derivative is found approximately.

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