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BITSAT Mathematics Application of Derivatives 2024 BITSAT 2024 (Memory Based Paper 3)

BITSAT Mathematics Question (2024) — Solution

Question

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

Options

  1. A. increasing in (0,1) (2, )
  2. B. increasing in (- , 0) (0,1)
  3. C. decreasing in (- , 0) (2, )
  4. D. decreasing in (0,1) (2, )

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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