Question

In which of the following intervals
$f\left(x\right)=2x^3-15x^2+36x+1$ is monotonic decreasing-

• A. $(-\infty ,2)$
• B. $(3,\infty$)
• C. $(0,3)$
• D. $(2,3)$

Answer 1

The correct option is D $(2,3)$

$f\left(x\right)=2x^3-15x^2+36x+1$
Since, $f\left(x\right)$ is monotonic decreasing , so $f^{\prime }\left(x\right)<0$
$f^{\prime }\left(x\right)=6x^2-30x+36<0$
$x^2-5x+6<0$
$x\in (2,3)$