Find the max rate of change of f at the given point and the direction in which it occurs.

$\displaystyle f(x, y, z) = \sqrt{x^{2} + y^{2} + z^{2}}, (3, 6, -2)$

Attempt:

$\displaystyle f_x = 0.5(x^2 + y^2 +z^2)^{-0.5}2x$

$\displaystyle =0.5(3^{2} + 6^{2} + 4)^{-0.5}6$

$\displaystyle = 0.43$

$\displaystyle f_y = 0.5(x^2 + y^2 +z^2)^{-0.5}2y$

$\displaystyle =0.5(3^{2} + 6^{2} + 4)^{-0.5}12$

$\displaystyle = 0.86$

Gradient vector at $\displaystyle (x, y) = (f_x, f_y) = (0.43, 0.86)$

How would you find the direction in which f occurs?