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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.

The maximum value of directional derivative of f occurs

Understand how to find the maximum value of a directional derivative of a function. This problem covers key vector calculus concepts such as the gradient and the dot product. Suitable for undergraduate students studying multivariable calculus and vector analysis.

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