A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Let \(f\) be a function satisfying \(f(x+y) = f(x) + f(y) \forall x,y\) and if \(f(x) = x^2 g(x)\) where \(g(x)\) is a continuous function, then find \(f'(x)\).

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

    i am going to make a guess, that \[f'(x)=c\] some constant. not sure what that has to do with \[f(x)=x^2g(x)\] but if i recall correctly the only function satisfying the first condition is \[f(x)=cx\]

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

    \[f'(x)=2xg(x)+x^2g'(x)\]

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

    @zed that is true for any f, right?

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

    i don't think there are any functions that satisfy \[f(x+y)=f(x)+f(y)\] other than constant multiples

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

    Here, these are the options 1. g'(x) 2. g(0) 3. g(0) + g'(x) 3. 0

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

    multiple choice?

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

    looks like zero to me

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

    yeah, but i am clueless

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

    really? why. i am fairly certain \[f'(x)=c\] a constant

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

    us the definition of the derivative

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

    *use

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

    (f(x+h)-f(x))/h (f(x)+f(h)-f(x))/h =f(h)/h

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

    \[f(h)=h^2g(h)\]

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

    \[\frac{h^2g(h)}{h}=hg(h)\] take limit as h goes to zero...use squeeze theorem

  15. 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.