HELP!! What are the intervals for the increasing and decreasing of this graph??

See the attached two images to visually see where the function is increasing and decreasing.  (There's one image for each.)

We identify where a function is increasing based on where the y-values increase as the x-values increase.  In other words, as you move left-to-right, the function is increasing if the function is moving upwards.

We identify where a function is decreasing based on where the y-values decrease as the x-values increase.  In other words, as you move left-to-right, the function is decreasing if the function is moving downwards.

In both cases, while you recognize where it's one or the other based on the y-values, you describe it based on where it's happening, based on the x-values.  The y-values tell you what's happening, the x-values tell you where it's happening.

The function is increasing on the intervals (-infinity, -4) and (-2,infinity).  This is the red highlighted portions.

The function is decreasing on the interval (-4,–2).  This the the blue highlighted portions.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.