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

Ldaniel

If f(x) ≤ g(x) on the interval [a, b], then the average value of f is less than or equal to the average value of g on the interval [a, b]. True or False

  • one year ago
  • one year ago

  • This Question is Closed
  1. tkhunny
    Best Response
    You've already chosen the best response.
    Medals 0

    Couple of ways to go about it, I suppose. Can you write an expression that represents the average value on the interval?

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

    how?

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

    Area = Height * Width or, in this case Area = (Average Height) * Width Are you seeing how to do it?

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

    so its true?

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

    ?? How did you get to that? We haven't done anything, yet. Generally, we call this guessing, but you may be going on evidence that you are not sharing. How do you find the area under a curve on a Cartesian Coordinate system?

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

    we don't have real values so i just used a and b

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

    Every continuous function has an antiderivative right?

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

    Yes. I'm pretty excited to see where you are going with that. It's important to point out that we may not be able to write the antiderivative. We just need to know that it exists.

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

    yes to what?

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

    If F(x) is an antiderivative of f(x) and G(x) = F(x) + 2, then G(x) is an antiderivative of f(x) right? or am i wrong?

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

    So close. G and F are not necessarily related. Let's back up just a hair. We can calcualte the average value of f(x) on the interval [a,b] using the integral and that rectangle formula. Average Value of f(x) on [a,b] = \(\dfrac{\int\limits_a^b f(x)\;dx}{b-a}\). Do you see how htat works?

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

    yea

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

    And, as you very correctly pointed out, \(\int\limits_a^b f(x)\;dx = F(b) - F(b)\), where \(F(x)\) is an antiderivative of \(f(x)\). Still making sense?

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

    yea

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

    If f(x) ≤ g(x) on the interval [a, b], then the average value of f is less than or equal to the average value of g on the interval [a, b]. Well, then, all we know is \(f(x) \le g(x)\) and we are trying to prove that \[\dfrac{F(b) - F(a)}{b-a} \le \dfrac{G(b) - G(a)}{b - a}\]. Can we do it?

    • one year 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.