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AP EAMCET202119 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

Which statement among the following is true? (i) The function f ( x ) = x | x | is strictly increasing on R - 0 . (ii) The function f ( x ) = log ( 1 / 4 ) x is strictly increasing on ( 0 , ∞ ) . (iii) A one-one function is always an increasing function. (iv) f ( x ) = x 1 / 3 is strictly decreasing on R

Options

  1. Ai
  2. Bi i
  3. Ci i i
  4. Di v

Correct answer

A. i

Step-by-step solution

i Given that f x   =   x x Differentiate on both sides f ' x   =   x x x   +   x f ' x   =   2   x f ' x   >   0   ∀   x   ∈   R   -   0 So f x is strictly increasing function. So it's true. i i f x   =   log 1 4 x Differentiating on both sides f ' x   =   1 x log 1 4   =   - 1 x log 4 ⇒ f ' x     <   0   ∀   x   ∈ &#16

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