anonymous
  • anonymous
f(x) = ln x, [1, 8] Using mean value theorem, find all numbers c that satisfy the conclusion of the Mean Value Theorem.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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myininaya
  • myininaya
\[f'(c)=\frac{f(b)-f(a)}{b-a}\]
anonymous
  • anonymous
I found my c to be 3.366 but the answer is wrong
myininaya
  • myininaya
a=1 and b=8

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anonymous
  • anonymous
yes, i know how to do it..but got it wrong.. don't know why
myininaya
  • myininaya
Does it want an approximation?
anonymous
  • anonymous
it didn't say..so i'm thinking should the answer be an exact number
anonymous
  • anonymous
(Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).
anonymous
  • anonymous
but then i think there is only 1 number c
myininaya
  • myininaya
Well the number you put above is not the exact answer
myininaya
  • myininaya
That is call an appoximation
anonymous
  • anonymous
how do get an exact number?
myininaya
  • myininaya
So I assume you did the setup right because you got the approximation to the correct answer
myininaya
  • myininaya
This is the setup you chose? \[\frac{1}{c}=\frac{\ln(8)-\ln(1)}{8-1}\]
anonymous
  • anonymous
yes
myininaya
  • myininaya
We know ln(1) =? and 8-1=? So can you tell me what 1/c= Don't use your calculator
anonymous
  • anonymous
and then f'(c) = 1/c then solve for c
anonymous
  • anonymous
ln 1 = 0 8-1= 7
myininaya
  • myininaya
Ok we have \[\frac{1}{c}=\frac{\ln(8)-0}{7}\] Do you know how to solve this for c?
anonymous
  • anonymous
ln 8/ 7 = 1/c c= 7/ln8
myininaya
  • myininaya
right
anonymous
  • anonymous
ok thanks so much!

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