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onegirl Group Title

Find all critical numbers and use the First Derivative Test to classify each as the location of a location maximum, local minimum, or neither. y = x^4 + 4x^3 - 2

  • one year ago
  • one year ago

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  1. onegirl Group Title
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    @electrokid can u help?

    • one year ago
  2. electrokid Group Title
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    using our previous discussions, you can start the work and I guide.

    • one year ago
  3. electrokid Group Title
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    step 1) first derivative \(y'=?\)

    • one year ago
  4. onegirl Group Title
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    Sorry i replied late i had internet issues. but the first derivative is 4x^2(x + 3)

    • one year ago
  5. electrokid Group Title
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    good. step 2) solve for "x": \(4x^2(x+3)=0\)

    • one year ago
  6. onegirl Group Title
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    okay i got x = -3 and x = 0

    • one year ago
  7. onegirl Group Title
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    are you there?

    • one year ago
  8. electrokid Group Title
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    good. those are the critical points. step 3) classify as maxima, minima or neither step 3.1) find second derivative of "f" -> find f''(x)

    • one year ago
  9. onegirl Group Title
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    how do i do that?

    • one year ago
  10. onegirl Group Title
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    are u there @electrokid

    • one year ago
  11. electrokid Group Title
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    step 3.1) find the second derivative.

    • one year ago
  12. onegirl Group Title
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    okay

    • one year ago
  13. onegirl Group Title
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    I got 12x^2 + 24x

    • one year ago
  14. PeterPan Group Title
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    Remember the critical points that you got? If the second derivative is positive when evaluated at one of those critical points, that critical point would be a local minimum. On the flip-side, if the second derivative is negative when evaluated at a critical point, that point would be a local maximum.

    • one year ago
  15. onegirl Group Title
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    so i substitute those critical point into the second derivative

    • one year ago
  16. PeterPan Group Title
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    Yes.

    • one year ago
  17. electrokid Group Title
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    yes. \(f''(x)=12x^2+24x\) step 3.2) plug in x=-3 in this equation and check the sign..

    • one year ago
  18. onegirl Group Title
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    okay

    • one year ago
  19. onegirl Group Title
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    i got 36

    • one year ago
  20. onegirl Group Title
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    and when i plugged in 0 i got 0

    • one year ago
  21. PeterPan Group Title
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    Okay, so, f''(-3) = 36 This is positive, therefore...?

    • one year ago
  22. onegirl Group Title
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    so it is a minimum?

    • one year ago
  23. PeterPan Group Title
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    a local minimum ;) What about f''(0) ?

    • one year ago
  24. onegirl Group Title
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    I got 0

    • one year ago
  25. PeterPan Group Title
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    It's neither positive nor negative, right?

    • one year ago
  26. onegirl Group Title
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    yes

    • one year ago
  27. PeterPan Group Title
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    Well, what does that mean, then?

    • one year ago
  28. onegirl Group Title
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    so it will be neither

    • one year ago
  29. PeterPan Group Title
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    It will be neither :D

    • one year ago
  30. onegirl Group Title
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    Okay thanks

    • one year ago
  31. electrokid Group Title
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    @PeterPan and @onegirl both did a great job and effort and both deserve a medal :) so, @onegirl give one to P-Pan ☮

    • one year ago
  32. PeterPan Group Title
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    Already done. ^.^

    • one year ago
  33. onegirl Group Title
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    lol I already did

    • one year ago
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