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
If $f(x)=k x^3-9 x^2+9 x+3$ is monotonically increasing in each interval, then
MathematicsApplication of DerivativesJEE Main
Options:
  • A $k \lt 3$
  • B $k \leq 3$
  • C $k\gt3$
  • D None of these
Solution:
2707 Upvotes Verified Answer
The correct answer is: $k\gt3$
$f^{\prime}(x)=3 k x^2-18 x+9=3\left[k x^2-6 x+3\right]\gt0, \forall x \in R$
$\therefore \Delta=b^2-4 a c \lt 0, k\gt0$ i.e., $36-12 k \lt 0$ or $k\gt3$

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.