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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