Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Christos

  • one year 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

  • This Question is Closed
  1. rulnick
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how did you find the -1/2

  3. rulnick
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    f''(x)=0 at x=-1/2

  4. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok and something more are my derivative calculations correct? f(x) = (2x +1)^3 f'(x) = 6(2x + 1)^2

  5. rulnick
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, all were perfect!

  6. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so its not decreasing that means its always increasing? Kinda what's the interval?

  7. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (0,infinity) increasing?

  8. rulnick
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    non-decreasing means increasing or flat. it is flat at the inflection point, increasing everywhere else

  9. rulnick
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so increasing on the entire real line except at -1/2, where it is flat (deriv=0)

  10. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, very nicely done

  12. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and decreasing interval*

  13. rulnick
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    empty set

  14. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    like I just say "it's not decreasing anywhere" ?

  15. rulnick
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  16. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Alright, thank you!

  17. rulnick
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    welcome

  18. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.