Mean-value theorem for integrals:

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Suppose that f is continuous on [a,b],Then there is a number c on [a,b] such that

$\displaystyle \int_a^b f(x)dx=(b-a)f(c)$

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My question:

I would like to prove that:

if f is a decreasing function on [a,b],then C less than or equal to (a+b)/2

Can you help me to do that??!

Thanks for any responding