Question

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)

Answer 1

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.

Answer 2

Thank you for your help.

Answer 3

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 <b>first</b> derivative:... "