Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

S Group Title

How to sketch the graph of f(x)=x^2(x^2-4) including the inflection point?

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    start with \[y=x^2(x-2)(x+2)\] so you see that you have 3 zeros, at x =-2,x=0,x=2

    • 2 years ago
  2. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    the zero at x = 0 has multiplicity 2, so the graph will touch the x - axis there but not cross it

    • 2 years ago
  3. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    to find the point of inflection you need the second derivative, \[f(x)=x^4-4x^2\] \[f'(x)=4x^3-8x\] \[f''(x)=12x^2-8\] set equal to zero and solve

    • 2 years ago
  4. S Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    My main question is that, when i find the inflection point I put square root of 2/3 into the original formula and i get -20/3 right?

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

    And this point can not be on the graph, this makes me confused

    • 2 years ago
  6. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, for the second coordinate you evaluate the function at \[\sqrt{\frac{2}{3}}\]

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

    yes, so I should get 2 inflection points

    • 2 years ago
  8. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    it must be on the graph, plug in the x, find the y

    • 2 years ago
  9. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    right \[\pm\sqrt{\frac{2}{3}}\]

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

    so when I plug I get - 20/3

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

    for point of inflection we need only to equate first derivative of f(x) to 0.not the second

    • 2 years ago
  12. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    actually it is the second first derivative gives relative max or min

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

    it should be plugged in the original formula, right?

    • 2 years ago
  14. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, original function you have the x, you want the y

    • 2 years ago
  15. S Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    correct

    • 2 years ago
  16. S Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    But in the end my inflection point comes up to be (- square root of 2/3 ; - 20/3) and (square root of 2/3 ; - 20/3) and my minimum points are (-2;-4) and (2;-4) and it seems that the point of inflection cant be on the graph

    • 2 years ago
  17. fazna Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but im sure that i can get the points of inflection from first derivative,not the second

    • 2 years ago
    • Attachments:

See more questions >>>

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.