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

Question

The interval in which the function f x = 2 x 2 - log x , for x > 0 decreases is, ( 2 , 4 ), 0 , 1 4, 1 2 , ∞, 0 , 1 2

MARKS App · Accepted Answer

Given: f x = 2 x 2 - log x f ' x = 4 x - 1 x Function is decreasing when f ' x 0 4 x - 1 x 0 ⇒ 4 x 2 - 1 0 ⇒ x 2 1 4 ⇒ x ∈ - 1 2 , 1 2 . But, x > 0 Therefore, f x is decreasing when x ∈ 0 , 1 2 .

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