1. The problem statement, all variables and given/known data Show that f(x) = x1x2 is a convex function on [a,ma]T where a [itex]\geq[/itex] 0 and m [itex]\geq[/itex] 1. 2. Relevant equations By definition f is convex iff [itex]\forall x,y\in \Re \quad \wedge \quad \forall \lambda :\quad 0\le \lambda \le 1\quad \Rightarrow \quad f\left( \lambda x+(1-\lambda )y \right) \le \lambda f\left( x \right) +(1-\lambda )f\left( y \right)[/itex] 3. The attempt at a solution I am not really sure how to go about this. Firstly I was thinking on how to apply the above relation to multiple variables. I would assume that it applies in general and in this case x and y would be a vector of variables, but I still don't know how the proof follows. Also I am not sure is how the interval [a,ma]T plays into the equation.