Posted by Mike on .
Im having a hard time figuring out this problem:
Use the function, y=(x+1)^2 +2, to answer the following parts.
The increasing interval and decreasing interval
To find both I believe that:
increasing : x < 1
decreasing : x > 1
So is this on solution below
Increasing interval (4,7)
Decreasing interval(2,7)

Algebra 
MathMate,
The increasing and decreasing intervals depend on the second derivative:
f'(x)=dy/dx;=2(x+1)
If f'(x)>0, the function is increasing.
If f'(x)<0, the function is decreasing.
Since f'(x)=0 at x=1,
f'(x)>0 for (∞1], and
f'(x)<0 for [1,∞)
The increasing and decreasing intervals can be deduced.
Note that x=1 is included in both intervals. If this is not clear why, look up the definition of increasing and decreasing intervals, or post. 
Algebra 
Mike,
Thank you for your help.

Algebra :) 
MathMate,
You're welcome!
Sorry, there is a typo in my response, although it does not affect the results.
The first sentence should read:
"The increasing and decreasing intervals depend on the first derivative:... "