A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Consider x^2 on an interval [0,1/2]. The Mean Value theorem suggest that there is a number c in (0.1/1/2) such that f'(c) is equal to a particular d.What is d?

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

    find the slope of the secant line that passes through (.1, .01) and (.5, .25)

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

    sorry, my browser crashed

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

    is the interval [0, 1/2] or [0.1, 1/2]?

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

    well, I'll assume [0, 1/2] then. Let's say f(x) = x^2

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

    Then the slope of the line between (0, f(0) and (.5, f(.5)) is (.25-0)/(.5-0) = 0.5

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

    next find where the derivative equals 0.5. This is the point where the tangent line is parallel to the secant line between (0, f(0) and (.5, f(.5))

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

    sorry I crashed too haha

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

    so f'(x) = 2x = 0.5 x = 0.25

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

    so is d 0.25?

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

    yes

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

    well, no actually

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

    d is 0.5

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

    oh k, that makes more sense

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

    because f'(0.25) = 0.5 so c = 0.25 d = 0.5

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

    thanks a lot

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

    no problem

  17. 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.