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onegirl Group Title

For what intervals is f(x) = 2x^4 – 4x^2 + 6 increasing? A. The graph is increasing on the intervals (-1, 0) and (1, ∞). B. The graph is increasing on the interval (1, ∞). C. The graph is increasing on the interval (-1, 0). D. The graph is increasing on the intervals ( -∞ , -1) and (0, 1).

  • one year ago
  • one year ago

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  1. bfsgd Group Title
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    You can differentiate the function and it is increasing if f ' (x)>0.

    • one year ago
  2. onegirl Group Title
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    huh?

    • one year ago
  3. onegirl Group Title
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    @electrokid can u help?

    • one year ago
  4. bfsgd Group Title
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    Differentiating f(x) we get \[f'(x)=8x^3 - 8x=8x(x^2-1)\] That is positive for all x>1.

    • one year ago
  5. onegirl Group Title
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    ok

    • one year ago
  6. onegirl Group Title
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    so what do i do next?

    • one year ago
  7. bfsgd Group Title
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    That's it :)

    • one year ago
  8. onegirl Group Title
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    ohh so it will be D?

    • one year ago
  9. bfsgd Group Title
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    No...D includes negative numbers. You need the one thats only x>1.

    • one year ago
  10. electrokid Group Title
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    |dw:1364917996121:dw| get the critical points you see the four intervals? take an arbitrary number from each interval and check the signs of the derivative

    • one year ago
  11. onegirl Group Title
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    Ohh so its B

    • one year ago
  12. bfsgd Group Title
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    Yep :)

    • one year ago
  13. electrokid Group Title
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    nope

    • one year ago
  14. onegirl Group Title
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    what do you mean nope?

    • one year ago
  15. onegirl Group Title
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    so its wrong?

    • one year ago
  16. bfsgd Group Title
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    Its right....

    • one year ago
  17. electrokid Group Title
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    yep. B is not the answer

    • one year ago
  18. electrokid Group Title
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    check the interval (-1,0)

    • one year ago
  19. electrokid Group Title
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    in math, there are no shortcuts. follow the "yellow brick road"

    • one year ago
  20. onegirl Group Title
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    ok

    • one year ago
  21. electrokid Group Title
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    do you see the mistake?

    • one year ago
  22. onegirl Group Title
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    yea

    • one year ago
  23. electrokid Group Title
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    so, what is the answer?

    • one year ago
  24. onegirl Group Title
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    i got C

    • one year ago
  25. electrokid Group Title
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    follow the steps. did you use the number line that I drew?

    • one year ago
  26. onegirl Group Title
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    yea hold on

    • one year ago
  27. onegirl Group Title
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    so the critical points are -1, 0 and 1

    • one year ago
  28. onegirl Group Title
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    okay

    • one year ago
  29. electrokid Group Title
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    sorry. yes. you are correct. "3" points, -1, 0 and 1

    • one year ago
  30. onegirl Group Title
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    lol ok

    • one year ago
  31. electrokid Group Title
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    |dw:1364919097503:dw|

    • one year ago
  32. electrokid Group Title
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    interval (-inf, -1) plug in x=-2 and find f'(x)

    • one year ago
  33. onegirl Group Title
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    plug in -2 into the problem?

    • one year ago
  34. electrokid Group Title
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    yep

    • one year ago
  35. onegirl Group Title
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    into (x - 2)^2?

    • one year ago
  36. electrokid Group Title
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    into the entire thing f'(x)

    • one year ago
  37. onegirl Group Title
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    ok

    • one year ago
  38. onegirl Group Title
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    idk i got 16?

    • one year ago
  39. onegirl Group Title
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    and the derivative i got 0

    • one year ago
  40. electrokid Group Title
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    \[f'(-2)=8(-2)[(-2)^2-1]=?\]

    • one year ago
  41. onegirl Group Title
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    ohh i got -48

    • one year ago
  42. electrokid Group Title
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    good.|dw:1364919435696:dw| now, we check interval (-1,0) find \[f'(-0.5)\]

    • one year ago
  43. onegirl Group Title
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    okay i get 0

    • one year ago
  44. electrokid Group Title
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    nope try again.

    • one year ago
  45. onegirl Group Title
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    you mean find the derivative of -0.5 ?

    • one year ago
  46. electrokid Group Title
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    derivative "at" x=-0.5

    • one year ago
  47. onegirl Group Title
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    ohhh ok

    • one year ago
  48. electrokid Group Title
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    yep. what did you get?

    • one year ago
  49. onegirl Group Title
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    i'm still getting 0 :/

    • one year ago
  50. electrokid Group Title
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    \[f'(-0.5)=8(-0.5)[(-0.5)^2-1]=?\]

    • one year ago
  51. onegirl Group Title
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    ok i get 3

    • one year ago
  52. electrokid Group Title
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    good.|dw:1364919843444:dw| now we check interval (0,1) lets take x = 0.5 similarly, find \[f'(0.5)\]

    • one year ago
  53. onegirl Group Title
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    okay

    • one year ago
  54. onegirl Group Title
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    i get -3

    • one year ago
  55. electrokid Group Title
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    great |dw:1364919912982:dw| now the final interval (1,+infty) we take x= 2 \[f'(2)=?\]

    • one year ago
  56. onegirl Group Title
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    ok i get 48

    • one year ago
  57. electrokid Group Title
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    perfect. |dw:1364919991818:dw| now, f(x) is increasing when f'(x) >0 (i.e., f'(x) is positive) and f(x) is decreasing when f'(x) < 0 (i.e., f'(x) is negative)

    • one year ago
  58. electrokid Group Title
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    so, in what intervals do you see f'(x) positive?

    • one year ago
  59. onegirl Group Title
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    ok in 0,1 and 1, + infi

    • one year ago
  60. electrokid Group Title
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    great. which option says that?

    • one year ago
  61. onegirl Group Title
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    A!

    • one year ago
  62. electrokid Group Title
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    and that is your answer yay

    • one year ago
  63. onegirl Group Title
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    thanks :)

    • one year ago
  64. electrokid Group Title
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    follow the same procedure for the other one,

    • one year ago
  65. onegirl Group Title
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    ok

    • one year ago
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