Let I be an open interval where a<x<b\in I. Also, let f:I\rightarrow \mathbb{R} be differentiable.
Prove f is convex if and only if f(x)\geq f(a)+f'(a)(x-a) for all a,x\in I.

I have that the definition of convex is f(x)\leq L(x) where L(x)=f(a)+\frac{f(b)-f(a)}{b-a}(x-a)

I have tried to switch it around algebraically but I can't seem to figure it out. I'd appreciate any help.