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Christos

  • 2 years ago

f(x) = (2x +1)^3 f'(x) = 6(2x + 1)^2 f''(x) = 48x + 24 I need to know when its concave up/down increasing /decreasing and the inflection points I am new to this kind of stuff

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  1. rulnick
    • 2 years ago
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    First derivative is nonnegative for all real x, so f is non-decreasing. Second derivative is everywhere matching the sign of x+1/2, so there is an inflection point at x=-1/2. The function is concave down on x<-1/2 and concave up on x>-1/2.

  2. Christos
    • 2 years ago
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    how did you find the -1/2

  3. rulnick
    • 2 years ago
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    f''(x)=0 at x=-1/2

  4. Christos
    • 2 years ago
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    Ok and something more are my derivative calculations correct? f(x) = (2x +1)^3 f'(x) = 6(2x + 1)^2

  5. rulnick
    • 2 years ago
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    Yes, all were perfect!

  6. Christos
    • 2 years ago
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    so its not decreasing that means its always increasing? Kinda what's the interval?

  7. Christos
    • 2 years ago
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    (0,infinity) increasing?

  8. rulnick
    • 2 years ago
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    non-decreasing means increasing or flat. it is flat at the inflection point, increasing everywhere else

  9. rulnick
    • 2 years ago
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    so increasing on the entire real line except at -1/2, where it is flat (deriv=0)

  10. Christos
    • 2 years ago
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    here it asks me the open interval on which f is increasing what should I put? (-inf,-1/2)U(-1/2,int) ?

  11. rulnick
    • 2 years ago
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    yes, very nicely done

  12. Christos
    • 2 years ago
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    and decreasing interval*

  13. rulnick
    • 2 years ago
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    empty set

  14. Christos
    • 2 years ago
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    like I just say "it's not decreasing anywhere" ?

  15. rulnick
    • 2 years ago
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    yes

  16. Christos
    • 2 years ago
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    Alright, thank you!

  17. rulnick
    • 2 years ago
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    welcome

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