# Math Help - Convex functions

1. ## Convex functions

Suppose f and g are two increasing convex functions on [0,1] with $f(0) \leq g(0)$ and $f(1)=g(1)=1$. Show that
$(g'(x)-f'(x))(1-x) + g(x) - f(x) \geq 0$.

I know that $f(x)+(1-x)f'(x) \leq 1$, with the same for g. But that doesn't look that helpfull.

2. ## Re: Convex functions

I forgot to mention that f and g are polynomials with non-negative coefficients. I think it is sufficient that they are convex functions, but this maybe makes the problem easier?