What I learnt in class today:

A convex function \(f:\mathbb R\to\mathbb R\) is defined as satisfying

\(f(\lambda x + (1-\lambda )y)\leq \lambda f(x)+(1-\lambda )f(y) \quad \forall x,y\in \mathbb R,\ \forall \lambda \in [0, 1].\)

 

Thus, the shape of a convex function is like \(\smallsmile\) . An example of a convex function is f(μ)=μ²:

 

How clear is this post?