Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?
$Interval \rightarrow Function$
MathematicsApplication of DerivativesJEE MainJEE Main 2005
Options:
  • A
    $(-\infty, \infty) \rightarrow x^3-3 x^2+3 x+3$
  • B
    $[2, \infty) \rightarrow 2x^3-3 x^2-12 x+6$
  • 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:
1061 Upvotes Verified Answer
The correct answer is:
$\left(-\infty, \frac{1}{3}\right] \rightarrow \quad 3 x^2-2 x+1$
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.

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.