Home
Class 12
MATHS
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_(3)e`

D

`log_(e)3`

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-II ) Previous Year|8 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-II ) Previous Year ( Paragraph)|3 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 3 ( Subjective ) COMPREHENSION|4 Videos

  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

Similar Questions

Explore conceptually related problems

Verify mean value theorem for the function f(x)=x^(2)+4x-3 in the interval [-2,2]

Verify Lagrange's Mean Value Theorem for the functions : f(x)=log_(e)x in the interval [1, 2]

Knowledge Check

  • 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 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 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`

    • Similar Questions

    Explore conceptually related problems

    Verify the mean value theorem for the function f(x)=x^(2) in the interval [2,4]

    Find 'c' of Lagrange's Mean Value Theorem for the functions : f(x)=logx in the interval [1, e]

    Find c of Lagranges mean value theorem for the function f(x)=3x^(2)+5x+7 in the interval [1,3].

    Find the value of c in Mean Value theorem for the function f(x)=(2x+3)/(3x-2) in the interval [1,5] .

    Verify Lagrange's Mean value theorem for the function f(x) = x^(2) -1 in the interval [3,5].

    Home
    Profile