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



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myininaya
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\[f'(c)=\frac{f(b)f(a)}{ba}\]

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

myininaya
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a=1 and b=8

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

myininaya
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Does it want an approximation?

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

lovekblue
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(Enter your answers as a commaseparated list. If it does not satisfy the hypotheses, enter DNE).

lovekblue
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but then i think there is only 1 number c

myininaya
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Well the number you put above is not the exact answer

myininaya
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That is call an appoximation

lovekblue
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how do get an exact number?

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

myininaya
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This is the setup you chose?
\[\frac{1}{c}=\frac{\ln(8)\ln(1)}{81}\]

lovekblue
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yes

myininaya
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We know ln(1) =?
and 81=?
So can you tell me what 1/c=
Don't use your calculator

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

lovekblue
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ln 1 = 0
81= 7

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

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

myininaya
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right

lovekblue
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ok thanks so much!