Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathcalculus

  • 2 years ago

Locate all critical points of s(t) = (2 t - 3)^(2) (8 - 2 t)^(3)?

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

    Ok is this a calc problem?

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

    yes

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

    @Paynesdad

  4. Paynesdad
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    SO your critical points are max, min, and points of inflection, right?

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

    critical points are x

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

    we have to solve for x... to find the y's and that gives us our point

  7. Paynesdad
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Right but when the question says critical points...In calculus that is usually the maximum, minimum an/or points of inflection.

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

    \[s(t)=(2t-3)^2(8-2t)^3\\ \Rightarrow~s'(t)=4(2t-3)(8-2t)^3-6(2t-3)^2(8-2t)^2\\ \Rightarrow~s'(t)=(2t-3)(8-2t)^2\left[4(8-2t)-6(2t-3)\right]\\ \Rightarrow~s'(t)=(2t-3)(8-2t)^2(50-20t)\] It should be fairly easy to find when \(s'(t)=0\).

  9. Paynesdad
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That would locate your max and minimums but not your points of inflection. @SithsAndGiggles

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

    @Paynesdad, usually when a problem asks for critical points, it's referring to the critical points of \(f(x)\). Points of inflection for \(f(x)\) are critical points of \(f'(x)\), not \(f(x)\), so I would think that's the assumption to be used here.

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

    @SithsAndGiggles we used the product AND chain rule right?

  12. Paynesdad
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yep

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

    Product, chain, power (not necessarily in that order).

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

    @Paynesdad, but that doesn't mean critical points can't be inflection points. Depends on the function.

  15. Paynesdad
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Correct .. I just wanted to know if she would need to go on and get the 2nd derivative to find the points of inflection as well or just the first derivative critical points.

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

    @Paynesdad oh sorry, no i was only looking for the critical points.

  17. Paynesdad
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sounds like you have a good handle on this problem...Nice work @SithsAndGiggles and @mathcalculus

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.