A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Rizags

  • one year ago

If f is differentiable at 1, and the limit of f(1+h)/h as h->0 is 5, what is f(1)?

  • This Question is Closed
  1. Rizags
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ` f is differentiable at 1` so \[\Large \lim_{h\to 0}\frac{f(1+h)-f(1)}{h}\] exists and it is defined based on the limit definition of the derivative

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

    so \[f'(1) = 5-\lim_{h \rightarrow 0}\frac{f(1)}{h}\]

  4. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Large \lim_{h\to 0}\frac{f(1+h)}{h}=5\] \[\Large \lim_{h\to 0}\frac{f(1+h){\LARGE \color{red}{-0}}}{h}=5\] \[\Large \lim_{h\to 0}\frac{f(1+h){\LARGE \color{red}{-f(1)}}}{h}=5\] so we see that \(\Large f(1) = 0\)

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

    so my step would be invalid?

  6. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    it's valid, I just don't see where to go with it

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

    oh ok. And you knew to put in that f(1) as 0 simply because the equation resembled the derivative limit?

  8. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I saw it match up with the limit definition. Well almost match up. It was just missing the `-f(1)` part

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

    so f(x) = 0 and f'(x) = 5?

  10. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    f ' (1) = 5 and f(1) = 0 we can't say anything about f(x) or f ' (x) in general

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

    ok, thank you

  12. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    IF it was \[\Large \lim_{h\to 0}\frac{f(x+h)-f(x)}{h}=5\] then we can say f ' (x) = 5

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

    ok got it

  14. 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.