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Question
Verify Lagrange’s mean value theorem for the function f(x)=x+1/x, x ∈ [1, 3]
Solution
step 1:
Given
`f(x)=x+1/x, x ∈ [1, 3]`
`f'(c)=(f(3)-f(1))/(3-1)`
`f(x)=x+1/x`
`f(3)=10/3`
`f(1)=2`
`f'(x)=1-1/x^2`
`f'(c)=1-1/c^2`
`1-1/c^2=(10/3-2)/2`
`(c^2-1)/c^2=2/3`
`3c^2-3=2c^2`
`c^2=3`
`c=sqrt3`
`c in (1,3)`
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