Posted by **Matthew** on Saturday, November 10, 2007 at 7:19pm.

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 dont understand neither so i cant do the question! please help!

- CALCULUS! -
**bobpursley**, Saturday, November 10, 2007 at 7:48pm
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

## Answer this Question

## Related Questions

- Calculus - Given f(x) = -1/x, find all c in the interval [-3, -½] that satisfies...
- calculus - Let f(x) = (x+1)/(x-1). Show that there are no vlue of c such that f(...
- math - Suppose f(x) = x^3 on the interval [1, 4]. Use the Mean Value Theorem to ...
- calc - Use the Mean Value Theorem to show: -x < sinx < x for all x > 0...
- Calculus - Consider the function f(x)=6x-cos(x)+5 on the interval 0 is less than...
- Calculus - Find all values for c in the intercal (1,4) so that the slope of the ...
- calculus - let f(x)= (x-3)^-2 Show that there is no value of c in (1,4) such ...
- Calculus - Suppose f(x)= 7-8x^2, by the Mean Value Theorem, we know there exists...
- calculus - determine whether the mean value theorem can be applied to f on the ...
- Calculus - Verify the hypothesis of the mean value theorem for each function ...