Posted by Mike on Thursday, May 5, 2011 at 9:09am.
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, Thursday, May 5, 2011 at 9:27am
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, Thursday, May 5, 2011 at 9:34am
Thank you for your help.

Algebra :)  MathMate, Thursday, May 5, 2011 at 12:07pm
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:... "
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