```markdown
The image is a diagram illustrating optimization concepts. It features:

- A point labeled \( x \).
- An arrow originating from \( x \), indicating the direction of \(-\nabla f(x)\).
- Dashed contour lines representing levels of the function \( f \).
- An ellipse centered at \( x \), defined by the equation \(\{x + v \mid v^T \nabla^2 f(x) v = 1\}\).
- Two points marked as \( x + \Delta x_{nsd} \) and \( x + \Delta x_{nt} \).
- Text indicating that \(\Delta x_{nt}\) is the steepest descent direction at \( x \) in the local Hessian norm.
- The mathematical expression for the norm: \(\|u\|_{\nabla^2 f(x)} = (u^T \nabla^2 f(x) u)^{1/2}\).

Additional text notes that the dashed lines are contour lines of \( f \), and the arrow shows \(-\nabla f(x)\).
```
