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

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cosinusix | College Teacher | (Level 3) Assistant Educator

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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`

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