Q. The function $f(x) = 2x^{3} + 3x^{2} - 12x + 1$ decreases in the interval
A) (2, 3)
B) (1, 2)
C) (-2, 1)
D) (-3, -2)
Explanation
(c)
Given, $f(x) = 2x^{3} + 3x^{2} - 12x + 1$
$\Rightarrow f^{'}(x) = 6x^{2} + 6x - 12$
For $f(x)to$ be decreasing, $f^{'}(x) < 0$
$\Rightarrow 6(x^{2} + x - 2) < 0$
$\Rightarrow (x + 2)(x - 1) < 0$
$\Rightarrow x \in ( - 2,1)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.