Consider the function $f \left( x, y \right) = -3x^2 + y^2$.
Find the the directional derivative of $f$ at the point $\left( -3, 3 \right)$ in the direction given by the angle $\theta = \frac{\pi}{3}$.

Find the unit vector which describes the direction in which $f$ is increasing most rapidly at $\left( -3, 3 \right)$.

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