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

Question

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

myininaya · Answer

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

anonymous · Answer

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

myininaya · Answer

a=1 and b=8

anonymous · Answer

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

myininaya · Answer

Does it want an approximation?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

but then i think there is only 1 number c

myininaya · Answer

Well the number you put above is not the exact answer

myininaya · Answer

That is call an appoximation

anonymous · Answer

how do get an exact number?

myininaya · Answer

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

myininaya · Answer

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

anonymous · Answer

yes

myininaya · Answer

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

anonymous · Answer

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

anonymous · Answer

ln 1 = 0
8-1= 7

myininaya · Answer

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

anonymous · Answer

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

myininaya · Answer

right

anonymous · Answer

ok thanks so much!