The interval in which the function f x = 2 x 2 - log x , for x > 0 decreases is

The interval in which the function fx=2x2-logx, for x>0 decreases is
  1. (2,4)
  2. 0,14
  3. 12,∞
  4. 0,12

Solution

Given:

fx=2x2-logx

f'x=4x-1x

Function is decreasing when f'x<0

4x-1x<0

⇒4x2-1<0

⇒x2<14

⇒x∈-12,12.

But, x>0 

Therefore, fx is decreasing whenx∈0,12.

Asked in: AP EAMCET 2018 (25 Apr Shift 1)

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