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)
The increasing and decreasing intervals depend on the second derivative:
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.
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:... "