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BITSAT2024MathematicsApplication of DerivativesActual

Consider the function f(x)= |x-1| x^2 , then f(x) is

Options

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

Correct answer

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

Step-by-step solution

Given, f(x)= aligned x-1 x^2 ; & x 1 -x+1 x^2 ; & x 1 aligned . aligned & f(x)= cases 1 x - 1 x^2 ; & x 1 - 1 x + 1 x^2 ; & x 1 cases & f^ (x)= cases -1 x^2 + 2 x^3 ; & x 1 1 x^2 - 2 x^3 ; & x 1 cases & f^ (x)= cases 2-x x^3 ; & x 1 x-2 x^3 ; & x 1 cases aligned By observation, f^ (x) will be Decreasing in (0,1) (2, ) and increasing in (- , 0) (1,2)

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