```markdown
## Properties

### Modified Jensen Inequality
For a quasiconvex function \( f \):

\[ 0 \leq \theta \leq 1 \implies f(\theta x + (1 - \theta)y) \leq \max\{f(x), f(y)\} \]

### First-Order Condition
A differentiable function \( f \) with a convex domain is quasiconvex if and only if:

\[ f(y) \leq f(x) \implies \nabla f(x)^T (y - x) \leq 0 \]

### Diagram
- A contour plot with a point labeled \( x \) and a gradient vector \( \nabla f(x) \).

### Note
Sums of quasiconvex functions are not necessarily quasiconvex.

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