Algebra
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)

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. 
Thank you for your help.

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:... "