Question

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

Answer: (D)

$( - \infty , 1] \cup [3, \infty)$

Answer 2

$f\left(x\right)=x^{3}-6x^{2}+9x+10$
$f '\left(x\right)=3x^{2}-12x+9$
$f '\left(x\right)=0$
$3x^{2}-12x+9=0 \quad$(dividing by $3$)
$x^{2}-4x+3=0$
$x^{2}-3x-x+3=0$
$x\left(x-3\right)-1\left(x-3\right)=0$
$x=3, 1$
$(-\infty, 1 ] \cup[3,\infty)$