## anonymous 3 years ago f(x) = ln x, [1, 8] Using mean value theorem, find all numbers c that satisfy the conclusion of the Mean Value Theorem.

1. myininaya

$f'(c)=\frac{f(b)-f(a)}{b-a}$

2. anonymous

I found my c to be 3.366 but the answer is wrong

3. myininaya

a=1 and b=8

4. anonymous

yes, i know how to do it..but got it wrong.. don't know why

5. myininaya

Does it want an approximation?

6. anonymous

it didn't say..so i'm thinking should the answer be an exact number

7. anonymous

(Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).

8. anonymous

but then i think there is only 1 number c

9. myininaya

Well the number you put above is not the exact answer

10. myininaya

That is call an appoximation

11. anonymous

how do get an exact number?

12. myininaya

So I assume you did the setup right because you got the approximation to the correct answer

13. myininaya

This is the setup you chose? $\frac{1}{c}=\frac{\ln(8)-\ln(1)}{8-1}$

14. anonymous

yes

15. myininaya

We know ln(1) =? and 8-1=? So can you tell me what 1/c= Don't use your calculator

16. anonymous

and then f'(c) = 1/c then solve for c

17. anonymous

ln 1 = 0 8-1= 7

18. myininaya

Ok we have $\frac{1}{c}=\frac{\ln(8)-0}{7}$ Do you know how to solve this for c?

19. anonymous

ln 8/ 7 = 1/c c= 7/ln8

20. myininaya

right

21. anonymous

ok thanks so much!