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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?

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# Homework Help: R twice continuously differentiable function proof

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