Question

The interval in which the function $f\left(x\right)=x^3-6x^2+9x+10$ is increasing in

• A. $[1,3]$
• B. $(-\infty ,1)\cup (3,\infty )$
• C. $(-\infty ,-1]\cup [3,\infty )$
• D. $(-\infty ,1]\cup [3,\infty )$

Answer 1

The correct option is D $(-\infty ,1]\cup [3,\infty )$

$f\left(x\right)=x^3-6x^2+9x+10$
$\Rightarrow f^{\prime }\left(x\right)=3x^2-12x+9=3(x-1)(x-3)$
$f^{\prime }\left(x\right)\ge 0$ in the interval $(-\infty ,1]\cup [3,\infty )$.
$\therefore f$ is increasing in $(-\infty ,1]\cup [3,\infty )$