For the function `f(x) = x + 1/x, x in [1,3]` , the value of c for mean value therorem is

Options

A. 1
B. `sqrt(3)`
C. 2
D. None of these

Answer

B

Explanation

Given `f(x)=x+1/x`
`impliesf'(x)=1-1/(x^(2)),f'(c)=(f(b)-f(a))/(b-a)`
`implies1-1/(c^(2))=([3+1/3]-[1+1/1])/(3-1)`
`implies(c^(2)-1)/(c^(2))=(10/3-2)/2`
`implies (c^(2)-1)/(c^(2))=4/(3xx2)=2/3`
`=3(c^(2)-1)=2c^(2)`
`implies 3c^(2)-2c^(2)=3`
`impliesc^(2)=3`
`impliesc+-sqrt(3)`
`:.c=sqrt(3)epsilon(1,3)`