What I learnt in class today:
A convex function 
![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].](http://s0.wp.com/latex.php?latex=f%28%5Clambda+x+%2B+%281-%5Clambda+%29y%29%5Cleq+%5Clambda+f%28x%29%2B%281-%5Clambda+%29f%28y%29+%5Cquad+%5Cforall+x%2Cy%5Cin+%5Cmathbb+R%2C%5C+%5Cforall+%5Clambda+%5Cin+%5B0%2C+1%5D.&bg=ffffff&fg=000&s=0 "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 
Convex functions
About the Author: Aidan Horn
Data analyst and labour economist. In my BSocSci, I majored in mathematics. I am involved with mathematical economics and econometrics, in my work in the School of Economics, at the University of Cape Town.
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