## lovekblue Group Title f(x) = ln x, [1, 8] Using mean value theorem, find all numbers c that satisfy the conclusion of the Mean Value Theorem. one year ago one year ago

1. myininaya Group Title

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

2. lovekblue Group Title

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

3. myininaya Group Title

a=1 and b=8

4. lovekblue Group Title

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

5. myininaya Group Title

Does it want an approximation?

6. lovekblue Group Title

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

7. lovekblue Group Title

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

8. lovekblue Group Title

but then i think there is only 1 number c

9. myininaya Group Title

Well the number you put above is not the exact answer

10. myininaya Group Title

That is call an appoximation

11. lovekblue Group Title

how do get an exact number?

12. myininaya Group Title

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

13. myininaya Group Title

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

14. lovekblue Group Title

yes

15. myininaya Group Title

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

16. lovekblue Group Title

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

17. lovekblue Group Title

ln 1 = 0 8-1= 7

18. myininaya Group Title

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

19. lovekblue Group Title

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

20. myininaya Group Title

right

21. lovekblue Group Title

ok thanks so much!