using Taylor to prove this inequality

lzt

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Joined
Dec 2, 2018
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3
Hi guys!

Immagine.jpg

I need to prove the last inequality using Taylor, knowing that f'(a)=f'(b)=0

Anyone can help me? Many thanks
 
I tried to use Taylor in xo=a, so that f(a+h)=f(a)+1/2*h^2*f''(a+theta*h)..

But now I don't know how to proceed.
 
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