Application of Derivatives
Monotonicity
JEE Main 2019
Grade 12
Question:
The function $f(x) = 2x^3 - 9x^2 + 12x + 1$ is increasing on:
(1) $(1, 2)$
(2) $(-\infty, 1) \cup (2,\infty)$
(3) $(-\infty, 1]$ only
(4) $[2,\infty)$ only
Step-by-Step Solution
Key Concept: Find $f'(x)$, factor it completely, and study the sign of $f'(x)$ on each of the intervals determined by its roots.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)