suppose that 3 <_ f prime of x <_ 5, for all values x. show that 18<_ f(8)-f(2) <_ 30

<_ signs mean less or equal to...

im supposed to apply mean value theorem or rolle's theorem... i don't understand neither so i cant do the question! please help!

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  1. If f'=3, then f=3x+C, so f(8)]=24+C, but C=2 if f'=3. So f(8)=26

    f(2)=8 by the same argument.

    then if f'x=3, f(8)-f(2)=26-8=>18

    You can make the same logic if f'=5, solve for C, then show that f(8)-f(2)<=30

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