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

`log _(3) e `

B

`log _(e) 3`

C

`2 log _(3) e`

D

`(1)/(2) log _(3) e`

Verified by Experts

The correct Answer is:

C

Using M.V.T. we can say f(c ) = `(f(b)-f(a))/(b-a)=(f(3)-f(1))/(2)`
`(1)/(c) = (log_(e)3)/(2) implies c = (2)/(log_(e)3)=2 log_(3) e`

Similar Questions

Explore conceptually related problems

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

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]

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

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

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].

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

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].