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anonymous

  • one year ago

Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 1 - (x - 6)^2 How would I solve this.

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  1. misty1212
    • one year ago
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    HI!!

  2. misty1212
    • one year ago
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    do you recognize it as a parabola?

  3. anonymous
    • one year ago
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    Hello, again.

  4. anonymous
    • one year ago
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    Yes.

  5. misty1212
    • one year ago
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    open up or down??

  6. anonymous
    • one year ago
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    Up

  7. misty1212
    • one year ago
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    hmmm

  8. misty1212
    • one year ago
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    \[f(x)=-(x-6)^2+1\]

  9. anonymous
    • one year ago
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    Oops, that's not what I graphed.

  10. misty1212
    • one year ago
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    try it you will see it opens down because the leading coefficient it negative

  11. anonymous
    • one year ago
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    Yes, I forgot about the negative.

  12. anonymous
    • one year ago
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    Alright, I have graphed it.

  13. misty1212
    • one year ago
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    you can see that it has a maximum when x = 6 it is increasing from \(-\infty\) to \(6\) and decreasing after that

  14. anonymous
    • one year ago
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    So, increasing x<6, decreasing x>6

  15. misty1212
    • one year ago
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    yes

  16. anonymous
    • one year ago
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    Thank you, Misty. You're very helpful.

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