Q. If $f(x) = 3x^{4} + 4x^{3} - 12x^{2} + 12$, then $f(x)$ is
A) Increasing in $( - \infty,\ - 2)$ and in (0, 1)
B) Increasing in (-2, 0) and in $(1,\ \infty)$
C) Decreasing in (-2, 0) and in (0, 1)
D) Decreasing in $( - \infty,\ - 2)$ and in $(1,\ \infty)$
Explanation
(b)
Since, $f(x) = 3x^{4} + 4x^{3} - 12x^{2} + 12$
$f^{'}(x) = 12x^{3} + 12x^{2} - 24x$
$= 12x(x - 1)(x + 2)$
For above it is clear that $f^{'}(x)$ increasing in (-2,0)and in (1,$\infty$)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.