The question reads:
Let $g$ be the function defined by $g(x,y,z) = 3x^2 y + z$. What is the best approximation of the directional derivative of $g$ at the point $(0,0,\pi)$ in the direction of the vector $(1,2,3)$...
The question then lists 5 different values. The question is 48 on test GR1768, for reference.
I dont understand why taking the partials $(6xy, 3x^2, 1)$ at the point and then taking the dot product with the vector $(1,2,3)$ is not correct.
One wants the direction vector normalized. So, normalizing, you'd get $(0,0,1) \cdot \frac{(1,2,3)}{(\sqrt{14}} \approx 0.8$.