r twice continuously differentiable function proof.... 1. The problem statement, all variables and given/known data Help if f:[a,b] [tex]\rightarrow[/tex] R is twice continuously differentiable, and f(x)[tex]\geq[/tex] 0 for all x in [a.b] and f ''(x) [tex]\leq[/tex] 0 for all x in [a,b] prove that 1/2 (f(a) + f(b)) (b-a) [tex]\leq[/tex] [tex]\int[/tex] f(x)dx [tex]\leq[/tex](b-a) f(a+b/2) (integral going from a to b) 2. Relevant equations -It's given that f is twice continuously differentiable. 3. The attempt at a solution By looking at the inequality I'm assuming that I have to use the mean value theorem somewhere.. But how?