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BITSAT2020MathematicsApplication of DerivativesActual

Consider the function f(x)=|x-1| /x², then f(x) is

Options

  1. Aincreasing in (0,1) (2, )
  2. Bincreasing in (- , 0) (1,2)
  3. Cdecreasing in (0,1) (2, )
  4. Ddecreasing in (0,1) (2, )

Correct answer

D. decreasing in (0,1) (2, )

Step-by-step solution

f(x)= |x-1| x² = array l 1-x x² , x 1 array . Clearly, f(x) is continuous for all x R except at x=0f^ (x)= array l x-2 x³ , x 1 array .f^ (x)>0 x 2 Hence, f(x) is increasing in (- , 0) (1,2) and decreasing in (0,1) (2, ) .

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