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JEE Main2005MathematicsApplication of DerivativesActual

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched? Interval Function

Options

  1. A(- , ) x^3-3 x^2+3 x+3
  2. B[2, ) 2x^3-3 x^2-12 x+6
  3. C(- , 1 3 ] 3 x^2-2 x+1
  4. D(- , -4] x^3+6 x^2+6

Correct answer

C. (- , 1 3 ] 3 x^2-2 x+1

Step-by-step solution

Clearly function f(x)=3 x^2-2 x+1 is increasing when f^ (x)=6 x-2 0 x [1 / 3, ) Hence (C) is incorrect.

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