Q100 / 225 · JEE Main 2005 · Mathematics

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

  • A
    $(-\infty, \infty) \rightarrow x^3-3 x^2+3 x+3$
  • B
    $[2, \infty) \rightarrow 2x^3-3 x^2-12 x+6$
  • Correct answer
    C
    $\left(-\infty, \frac{1}{3}\right] \rightarrow \quad 3 x^2-2 x+1$
  • D
    $(-\infty, -4] \rightarrow x^3+6 x^2+6$

Solution

Clearly function $f(x)=3 x^2-2 x+1$ is increasing when $f^{\prime}(x)=6 x-2 \geq 0 \Rightarrow x \in[1 / 3, \infty)$ Hence $(C)$ is incorrect.

Hence, the correct answer is option: 'C'.

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