. We have, ′ f ( ) = > ∀∈ ( , ) and ′ f ( ) = ∀∈− , ) and hence the proof is completed. - - Example . Prove that the function f x ( ) = is strictly increasing in ( , ¥ .
Since f x ( ) = , ′ > ∀∈ ∞ ( , . Hence f x ( ) is strictly increasing in ( , ¥ .