# Algebra

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)

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3. 👁 79
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.

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posted by MathMate
2. Thank you for your help.

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posted by Mike
3. You're welcome!

Sorry, there is a typo in my response, although it does not affect the results.

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

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posted by MathMate

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