VITEEE 2017 Paper

Using Lagrange's Mean Value Theorem Let f(x) be a function defined on [a, b]
then , f ' (c) =

f(b)−f(a)

b−a

... (i)
c ∊ [a , b]
∴ Given f (x) = logc c
∴ f ' (x) =

1

x

∴ equation (i) become

1

c

=

f(3)−f(1)

3−1

⇒

1

c

=

loge3−loge1

2

=

loge3

2

⇒ c =

2

loge3

⇒ c = 2log3e