```markdown
### Image Description

**Title:**
Optimality criterion for differentiable \( f_0 \)

**Content:**
- The text states that \( x \) is optimal if and only if it is feasible and:
  \[
  \nabla f_0(x)^T(y - x) \geq 0 \quad \text{for all feasible } y
  \]

- A diagram illustrates a feasible set \( X \), depicted as a shaded region.
- A point \( x \) is marked on the boundary of \( X \).
- The gradient \( \nabla f_0(x) \) is shown as a vector pointing outward from \( x \).
- Dashed lines represent level curves of \( f_0 \).
- The text below the diagram notes that if nonzero, \( \nabla f_0(x) \) defines a supporting hyperplane to the feasible set \( X \) at \( x \).

**Source:**
A. d'Aspremont. Convex Optimization M2.

**Page Number:**
42/67
```
