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onegirl

  • 2 years ago

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

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  1. onegirl
    • 2 years ago
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    @electrokid can u help?

  2. electrokid
    • 2 years ago
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    using our previous discussions, you can start the work and I guide.

  3. electrokid
    • 2 years ago
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    step 1) first derivative \(y'=?\)

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

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

  6. onegirl
    • 2 years ago
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    okay i got x = -3 and x = 0

  7. onegirl
    • 2 years ago
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    are you there?

  8. electrokid
    • 2 years ago
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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)

  9. onegirl
    • 2 years ago
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    how do i do that?

  10. onegirl
    • 2 years ago
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    are u there @electrokid

  11. electrokid
    • 2 years ago
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    step 3.1) find the second derivative.

  12. onegirl
    • 2 years ago
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    okay

  13. onegirl
    • 2 years ago
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    I got 12x^2 + 24x

  14. PeterPan
    • 2 years ago
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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.

  15. onegirl
    • 2 years ago
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    so i substitute those critical point into the second derivative

  16. PeterPan
    • 2 years ago
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    Yes.

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

  18. onegirl
    • 2 years ago
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    okay

  19. onegirl
    • 2 years ago
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    i got 36

  20. onegirl
    • 2 years ago
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    and when i plugged in 0 i got 0

  21. PeterPan
    • 2 years ago
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    Okay, so, f''(-3) = 36 This is positive, therefore...?

  22. onegirl
    • 2 years ago
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    so it is a minimum?

  23. PeterPan
    • 2 years ago
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    a local minimum ;) What about f''(0) ?

  24. onegirl
    • 2 years ago
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    I got 0

  25. PeterPan
    • 2 years ago
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    It's neither positive nor negative, right?

  26. onegirl
    • 2 years ago
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    yes

  27. PeterPan
    • 2 years ago
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    Well, what does that mean, then?

  28. onegirl
    • 2 years ago
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    so it will be neither

  29. PeterPan
    • 2 years ago
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    It will be neither :D

  30. onegirl
    • 2 years ago
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    Okay thanks

  31. electrokid
    • 2 years ago
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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 ☮

  32. PeterPan
    • 2 years ago
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    Already done. ^.^

  33. onegirl
    • 2 years ago
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    lol I already did

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