# find all numbers c that satisfy the conclusion of the Mean Value Theorem. f(x)=ln(x) interval= [1,4]

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### 1 Answer

The mean value is `(f(4)-f(1))/(4-1)=(ln(4)-0)/3=ln(4)/3`

`f'(x)=1/x`

In the mean value theorem, there exists c in (1,4) such that

`f'(c)=(f(4)-f(1))/(4-1) `

`1/c=ln(4)/3`

**Solution:** `c=3/ln(4)~~2.16`