CALCULUS!
posted by Matthew on .
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!

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)=268=>18
You can make the same logic if f'=5, solve for C, then show that f(8)f(2)<=30