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A value of c for which the conclusion of...

A value of c for which the conclusion of mean value theorem holds for the function `f(x) = log_(e) x` on the interval [1, 3] is:

A

`2 log_(3) e`

B

`1/2 log_(e) 3`

C

`log_(e)e`

D

`log_(e) 3`

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Knowledge Check

  • The value of c for which the conclusion of Lagrange's theorem holds for the function f(x) = sqrt(a^(2) - x^(2)) , a gt 1 on the interval [1,a] is

    A
    `(a (a+1))/(2)`
    B
    `(1 + a)/(2)`
    C
    `(sqrt(a (a + 1)))/(2)`
    D
    `(a (a-1))/(2)`

  • The value of c in Lagrange's mean value theorem for the function f(x)=log_ex in the interval [1,3] is

    A
    `2log_3e`
    B
    `1/2log_e3`
    C
    `log_3e`
    D
    `log_e3`

  • The mean value of the function f(x) = (1)/( x^2 + x) on the interval [1, 3//2] is

    A
    `log (6//5)`
    B
    `2 log (6//5)`
    C
    `4`
    D
    `log 3//5`

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