Question

Using Lagrange’s Mean Value Theorem show that

Answer 1

Answer:

Using Lagranges mean value theorem, prove that b-ab<log(ba)<b-aa,where 0<a<b. Solution : Lagranges Mean value theorem states that if a function f(x) is continuous and differentiable in interval (a,b), then, f(b)-f(a)b-a=f′(c), where c lies in (a,b).

Answer 2

Answer:

Lagrange’s mean value theorem (MVT) states that if a function

f

(

x

)

is continuous on a closed interval

[

a

,

b

]

and differentiable on the open interval

(

a

,

b

)

,

then there is at least one point

x

=

c

on this interval, such that

f

(

b

)

−

f

(

a

)

=

f

′

(

c

)

(

b

−

a

)

.

This theorem (also known as First Mean Value Theorem) allows to express the increment of a function on an interval through the value of the derivative at an intermediate point of the segment.