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For the function  where x ∈  consider the following two statements : 

(I) f is increasing in 

(II) f' is decreasing in 

Between the above two statements, 

  1. only (I) is true. 
  2. only (II) is true. 
  3. neither (I) nor (II) is true. 
  4. both (I) and (II) are true. 

Answer (Detailed Solution Below)

Option 1 : only (I) is true. 

Detailed Solution

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Calculation:

Given,  

⇒ 

⇒ 

= 

⇒  

∴ f is increasing in .

The correct answer is Option 1.

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