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## Homework Statement

Let [tex] f:[0,2]\rightarrow[0,\infty) [/tex] be continuous and non negative. Assume thaqt for any [tex] x,y\in[0,2] [/tex] and [tex] 0<\lambda<1 f(\lambda x+(1-\lambda)y)\geq\lambda f(x)+(1-\lambda)f(y) [/tex]. Given that f(1)=1 prove

[tex] \int_{0}^{2}f(x)dx\geq1 [/tex]

## The Attempt at a Solution

I've sat for hours. I have zero inspiration. I need a gentle shove in the right direction please.