Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

suju101

  • 2 years ago

guys help me find the concavity of f(x)= x^4-4x^3+4x^2. i kow the procedure but have problems with calculations. so helpp

  • This Question is Closed
  1. across
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Differentiate this function twice.

  2. ash2326
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    f(x)=x^4-4x^3+4x^2 f'(x)=4x^3-12x^2+8x f''(x)=12x^2-24x+8 let's find the inflection points where the curve changes concavity f''(x)=0 x=1+ 1/root 3 and 1-1/root 3 so x =0.42 and 1.577 here the curve changes concavity if f''(x)>=0 then f(x) is concave up if f''(x)<=0 then f(x) is concave down for the interval (-infinity, 0.42] and [1.577, infinity) f(x)''>=0 for the interval[0.42,1.577] f''(x)<=0 so f(x) has concavity up in the interval(-infinity, 0.42] and [1.577, infinity) and concavity down in [0.42, 1.577]

  3. suju101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it correct to get intervals in decimal??

  4. ash2326
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yeah, you can also write in radical like 1+1/root 3

  5. suju101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    plz help me with this f(x)=x^3/(3x^2+1). for the same thing. i messed up while solving.

  6. PROSS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1325942133129:dw| First step find the first derivative

  7. PROSS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    simplify

  8. PROSS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1325942270219:dw| simplify more

  9. PROSS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1325942373407:dw|

  10. PROSS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Now take the derivative again....

  11. PROSS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1325942535869:dw|

  12. PROSS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Simplify

  13. PROSS
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    set = to 0 and solve to determine possible points of inflection...then choose values to the left and right of these zeros to determine if x>0 concave up or if x<0 concave down....

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

    Search OpenStudy
    • 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.