The question is asking about the maximum value of the directional derivative of a function $f$.

The directional derivative of a function $f$ at a point in the direction of a vector $\mathbf{v}$ is given by the dot product:

$D_{\mathbf{v}} f = \nabla f \cdot \mathbf{v}$

Here, $\nabla f$ is the gradient of the function $f$, and $\mathbf{v}$ is the unit vector in the direction you're considering.

The maximum value of the directional derivative occurs when the vector $\mathbf{v}$ is in the same direction as the gradient $\nabla f$. This is because the dot product is maximized when the two vectors are aligned in the same direction, i.e., when $\mathbf{v}$ is parallel to $\nabla f$.

So, the correct answer is "In the direction of Grad f."

Let me know if you need more details or have any questions!

Here are 5 related questions:

1. What does the gradient $\nabla f$ represent geometrically?
2. Why is the directional derivative maximized in the direction of the gradient?
3. How is the curl $\mathbf{curl}(f)$ of a function related to the gradient and divergence?
4. In what physical situations would you be concerned with the directional derivative of a function?
5. How does the magnitude of the gradient relate to the rate of change of the function?

Tip: The gradient of a scalar field always points in the direction of the steepest ascent.