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March 30, 2017

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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 - ,

    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 - ,

    Thank you for your help.

  • Algebra :) - ,

    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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