Question

(b)
(1) identify the critical numbers of ( f ). (enter your answers as a comma - separated list.)
( x = - 1,0 )
(11) identify the open interval(s) on which ( f ) is increasing or decreasing. (enter your answer using interval notation.)
increasing ( (-infty, - 1) )
decreasing ( (0,infty) )

Explanation:

Step1: Analyze critical number behavior

The critical number is $x=-1$.

Step2: Test intervals for increasing/decreasing

For $x < -1$: The graph slopes downward, so $f$ is decreasing.
For $x > -1$: The graph slopes upward, so $f$ is increasing.

Answer:

(i) $x=-1$
(ii) increasing: $(-1, \infty)$
decreasing: $(-\infty, -1)$