Q. The value of $x$ for which the polynomial $2x^{3} - 9x^{2} + 12x + 4$ is a decreasing function of $x$, is
A) $- 1 < x < 1$
B) $0 < x < 2$
C) $x > 3$
D) $1 < x < 2$
Explanation
(d)
Let $f(x) = 2x^{3} - 9x^{2} + 12x + 4$
$\Rightarrow \ \ \ f^{'}(x) = 6x^{2} - 18x + 12$
$f^{'}(x) < 0$ for function to be decreasing
$\Rightarrow \ \ 6\left( x^{2} - 3x + 2 \right) < 0$
$\Rightarrow \ \ \ \left( x^{2} - 2x - x + 2 \right) < 0$
$\Rightarrow \ \ \ (x - 2)(x - 1) < 0$
$\Rightarrow \ \ 1 < x < 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.